The \bm command from package bm has both advantages and drawbacks over the \boldsymbol command from package amsbsy (loaded by amsmath). The first advantage of \bm is that it keeps the italic correction, so that something like \bm{T}_1^2 will look better than \boldsymbol{T}_1^2 (if you want to compare the two in a document, you must be careful that bm redefines \boldsymbol):

The second advantage is that \bm does not disrupt the spacing, whereas \boldsymbol does, even though it works correctly for binary operations (like +) and for relations (like =). As an example, here's the comparison between \boldsymbol{[}-1;1] and \bm{[}-1;1]:

However, \bm sometimes requires the user to add braces to avoid problems. For example, \bm{\dots} will provoke an error with amsmath, the solution being to type \bm{{\dots}}. Double accents also need to be enclosed in braces to work properly:
\documentclass{article}
\usepackage{amsmath,bm}
\begin{document}
%$\bm{\dots}$% causes an error
$\bm{\mathinner{\dots}}$% works
$\bm{\hat{\dot{\phi}}}$% does not work correctly
$\bm{{\hat{\dot{\phi}}}}$% works correctly
\end{document}

Finally, math alphabet nesting works better with \boldsymbol than with \bm. For example, here's the result of \mathrm{g\boldsymbol{g}} and \mathrm{g\bm{g}}:

\boldsymbol{T}_1^2one can use\boldmath${T}_1^2$\unboldmathinstead of\bm– Feb 08 '11 at 22:471and the2in bold (which may not be wanted) and will not work if you want it to appear inside a longer formula, e.g.$C+\int_a^b\bm{T}_1^2(t)dt$, where nothing else is in bold. – Philippe Goutet Feb 09 '11 at 09:20\boldmath$C+\bm{\int}_a^bT_1^2(t)dt$– Feb 09 '11 at 09:55\boldmathis fine, but if you want only one of the symbols of the formula to be in bold, you must use\bmor\boldsymbol(or\mathbf) on it and not touch anything else. It's in that case that the lack of italic correction is problematic with\boldsymbol. – Philippe Goutet Feb 09 '11 at 12:56\bmhas the italic correction. And it was me who said, thatboldmathcan do it, too ... – Feb 09 '11 at 13:00\bmhas italic correction whereas\boldsymbolhasn't. Although\boldmathhas it too, I wouldn't compare it to the other two since you can't use it for the same things. – Philippe Goutet Feb 09 '11 at 13:26\usepackage{newtxmath,newtxtext}instead. – Philippe Goutet Feb 25 '14 at 20:22\mathbold. So many options! Such a wealth of variety! – Reb.Cabin Nov 02 '18 at 15:32\bmdefault to italics? Is this the correct behaviour for equations? – Henrique Ferrolho May 30 '19 at 18:31\mathbffor upright bold math letters. There's no correct behaviour, it depends on what you want to achieve. Typographically speaking, putting widely used symbols in bold has never been a great practice as it can harm the color of the page if there are too many of them on a given page. – Philippe Goutet May 31 '19 at 10:30bmand wants to solve the\boldmath{[}problem you aptly pointed out, a workaround is:\mathopen{\boldsymbol{[}}-1;1]– Davislor Sep 10 '21 at 22:22