Legacy Forks of Computer Modern
Virtual Substitutes for European Computer Modern
When the Cork (T1) encoding came out in 1990, there were not yet any vector fonts supporting it, only bitmaps. METAFONT had been the original format used by DEK, and was considered sufficient to print out documents on paper. These original bitmap fonts were known as European Computer Modern (ec). (An alpha version had been called dc, and the TS1 companion font was originally tc. All fonts had extremely terse names back then, to keep their filenames short enough for MS-DOS.)
The state of the art back then for fonts, though, was the Adobe type 1 font format. The earliest hack to enable the T1 character encoding with vector fonts that came in a different character set were virtual fonts that remapped the vector font into a different character set. This was particularly necessary back when the other fonts on this list were still commercial products that did not come with the free distribution.
The most common of these was Lars Engebretsen’s ae, for Almost European. I still very occasionally see questions about it in 2022. Others versions were named ze, dm, zd and am.
Pros: Provide backward compatibility with some old source files.
Cons: Often missing a symbol, or falls back to a bitmap font. Copying from a PDF and pasting into another document fails. Virtual fonts are only understood by TeX. EC introduced an ugly Esszett that several other forks have, unfortunately, copied.
BaKoMa Fonts
These obsolete fonts were created by the late Basil K. Masilov in the early 1990s, and were among the first fonts to support the T1 (Cork) character set in the Adobe type 1 format. They were automatically converted from the METAFONT sources of the most popular TeX fonts of that time, using software written by Masilov. They are also available in OpenType and TrueType format. Formerly, the full font set was sold commercially and distributed as shareware.
Pros: A major technical advance at the time, supporting vector fonts in the full T1, TS1 and T2A encodings.
Cons: The most significant is poor hinting, causing extremely thin strokes that often did not scan well. Released under a non-free license.
Blue Sky Fonts
This version of Computer Modern was originally created by Blue Sky Research “around 1988” and converted into Postscript Type 1 format—with font hinting—by Y&Y in 1992. Whenever people talk about “the Blue Sky fonts,” they mean the versions made by Y&Y in the ’90s.
A great deal of effort went into making and hinting these fonts by hand. They were originally sold commercially by Blue Sky and then Y&Y, but are now free. They are the default font on PDFTeX.
Pros: They don’t make fonts like this any more. People especially don’t hint their fonts by hand. This collection also had a wide range of font sizes.
Cons: These only covered a limited repertoire of characters and were created in formats that are now obsolete.
European Modern
A now-obsolete version of the fonts above, once sold by Y&Y. CTAN still provides the support files for the command \usepackage[T1]{em} to work, if you have a copy of Y&Y’s files installed in your local TeX tree.
Pros: Allows older documents that use em.sty to run. Supported the Windows-1251 encoding, then the most widely-used in the world and still the assumed default for the Web, and the T1 encoding, the most popular for TeX, along with a few proprietary formats that tried to take the most-useful symbols from both. Uses the right Esszett.
Cons: Abandonware, made obsolete when Y&Y went out of business. Not included in the free release of the Y&Y TeX distribution, so modern distributions cannot legally use it. Only ever supported western European languages.
CM-Super
A collection of Computer Modern fonts autotraced from the METAFONT sources, with support for Cyrillic. They are normally recommended to be used with the fix-cm package. LaTeX uses this as its default version of cmr for several encodings, including T1.
Pros: Comprehensive support for the entire family in vector format.
Cons: You will need to juggle multiple 8-bit font encodings in your output, and the quality of these fonts (and of the automatic hinting) varies. Only supports Latin and Cyrillic. Copies the ugly Esszett from ec.
cbgreek
A conversion of Greek fonts by Silvio Levy, first to METAFONT, and then to the LGR encoding in Type 1 format. This effectively has been accepted as part of the Computer Modern family: several Unicode forks of it incorporate this package, and if you \usefont{LGR}{cmr}{m}{n} in a modern LaTeX system, this is what you get.
Pros: Does one thing excellently.
Cons: You will need to use a modern fork with more recent software.
Computer Modern Mathematical Blackboard Bold
This is technically a fork of Computer Modern, which also does one very specific thing excellently. It is an outline font tracing Computer Modern Bold Extended, for use as math symbols such as:
\documentclass{article}
\usepackage{cmathbb}
\begin{document}
[ \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R} \subset
\mathbb{C} \subset \mathbb{H} \subset \mathbb{O}
]
\end{document}

Pros: A superb blackboard bold font, much more visually consonant with Computer Modern than the one from AMS (which was based on Times, not Computer Modern). You might potentially also use it as a display font.
Cons: Has never, to my knowledge, been converted to OpenType.
MLModern
A slightly-darker variant of Latin Modern. For whatever reason, Computer Modern came out as darker and more legible in the original TeXbook than it does on modern PDF readers, or especially scans of printed documents, perhaps because the original rasterizer was programmed by DEK.
Pros: Heavier, if that’s what you want.
Cons: Only available in Type 1. Only supports Latin script and basic math symbols.
sansmathfonts
Extends Computer Modern Sans Serif with small caps, a bold slanted font and a math font.
Pros: See above.
Cons: Only comes in type 1, and only supports a limited range of symbols. Does not support an upright lowercase Greek math alphabet.
Other Miscellaneous Extensions
The ones accepted as de facto members of the extended family include the lh fonts for Cyrillic, two versions of IPA symbols from tipa, and the AMS math symbol extension fonts, but several other packages make some kind of cmr family available. For instance, the unofficially-contributed babel-georgian package makes cmr in its custom encoding an alias for the glyphs from DejaVu Serif (despite it not not looking similar at all). Some obsolete Hebrew packages have an odd set-up where you select between its four font families by selecting either the “normal,” “italic,” “bold” or “bold italic” shape and series, rather than giving them proper family names, and at least one user here liked it that way.
Pros: If you are still juggling legacy 8-bit font encodings with NFSS in this century (which some publishers still force you to do), and you switch to a font family that doesn’t support your language, there will be a default cmr font family to fall back to, and your document will still come out readable.
Cons: The quality varies widely.
OpenType Forks of Computer Modern
Computer Modern Unicode
These fonts are automatic conversions of the METAFONT versions of DEK’s fonts, using autotrace and fontforge. It also includes Cyrillic glyphs from lh, Greek from cbgreek, and IPA symbols from tipa.
Pros: Comprehensive conversions of TeX fonts from METAFONT to OpenType, including some such as Greek and the Concrete font family that were not included with Latin Modern.
Cons: The automatic hinting can cause it to display as spindly. Less hand-tuned than Latin Modern, and does not have some of its features, such as optical sizes. Less coverage than New Computer Modern. Some wonkiness in the font file causes Greek, particularly the letters λ and θ, to display incorrectly unless you activate the OpenType Greek script feature (whereas most newer fonts default to correct Greek text, and opt in to those variant forms with the Mathematical Greek feature). Copies the ugly Esszett from ec. No math support.
Latin Modern
A more hand-tuned conversion of Computer Modern to OpenType, by the same GUST user group in Poland that later extended this to the TeX Gyre fonts. The default with Unicode TeX engines.
Pros: A high-quality fork of the entire Computer Modern family, available in multiple formats to support every engine. Comes with free and open-source versions of all the standard PostScript fonts. Supports optical sizes and many other features out of the box.
Cons: Latin Modern Math has a very limited repertoire of symbols compared to other OpenType math fonts. Several bugs have not been fixed even after many years: the broken \setminus in Latin Modern Math comes up here perennially. Only supports Latin (some earlier versions had Cyrillic support that was removed). Some of the glyphs (such as the small caps) are not, in my opinion, as high in quality. You might agree or disagree with some of its changes, such as replacing \mathcal with one based on AMS Euler Calligraphic. No Book weight.
New Computer Modern
The most recent fork, by Antonis Tsolomitis of the University of the Aegean, with many features added to Latin Modern.
For some odd reason, a font that doesn’t resemble Computer Modern at all got thrown in as New Computer Modern Uncial.
Pros: Supports many more characters than any other version of Computer Modern, including the full set of Unicode math symbols and support for several languages such as Greek (based on Computer Modern Unicode’s conversion of cbgreek), Hebrew, Cherokee and Coptic. Has a number of character variants. Text fonts come in three weights: Bold, Regular and a slightly-heavier Book weight, similar to mlmodern, and the math font in Regular or Book.
Cons: Does not support PDFTeX. Only supports the equivalent of cmr, cmss and cmtt in two sizes, 8- and 10-point. Only the monospace family supports both italic and slanted shapes. The monospace Cyrillic italic face is poor quality..
Arabic Latin Modern Fixed
An extension to Latin Modern Mono that does an excellent job in its niche: a monospaced Arabic font to complement Latin Modern.
Related Fonts
DEK originally created Computer Modern as a clone of Monotype Modern 8A. Indeed, he projected its letters onto a large grid and had his students calculate the coordinates for METAFONT. This font (which is in the public domain, and is based on the earlier fonts Miller & Richards News 23 and 28, so there are no legal problems using it this way) was very similar to the Monotype Modern Series 7 font family that was widely preferred for mathematical texts up until World War II, when Monotype’s main production facility was converted to make munitions in 1939, and its office was destroyed by a German bomb on May 10, 1941. The Greek letters are similarly based on Porson, which Oxford University Press had used for its classic texts from DEK’s youth, originally because it had purchased the font for the Oxford English Dictionary. DEK had used this throwback font for the first edition of The Art of Computer Programming, and originally created TeX with the intention to typeset the complete series.
After the war, the company switched to a cheaper, less-flexible system and used Times as the main font. DEK was therefore consciously reviving the classic typesetting of a more civilized era.
Compare Computer Modern to Monotype Modern MT Pro Extended, which is still for sale. Similarly, compare the Greek math letters to GFS Porson.
mlmodern! – musarithmia Sep 08 '22 at 20:51\usepackge{lmodern}and\usepackage[T1]{fontenc}from my document, I getauto expansion is only possible with scalable fonts-- maybe that's from microtype? – Kerrek SB Sep 08 '22 at 21:55\copyrightsymbol which was rasterized with the CM fonts, but is vectorized with lmodern. With\copyrightand `\usepackage{microtype} you get the complaint about not being able to expand the non-scalable (raster) font.) – Kerrek SB Sep 08 '22 at 23:32mlmodernwould help future visitors know about it, in my opinion, as it is supposed to emulate how CM was supposed to look on paper. – Apoorv Potnis Sep 09 '22 at 20:19mlmodernis the best. Once I found it, I use it now all the time. I tried 100's of fonts, and this looks the best. Why? Because it is darker and in pdf is much clearer to read. default CM font is nice but too light and harder to read. These also work with lualatex. Had no problem, even though it is supposed to work only in pdflatex. – Nasser Sep 10 '22 at 08:49