For years I've been using HTML to produce web pages with text flowing nicely around images. Here's an example of the sort of thing:
As you can see, the images are floated left and right, and may overlap in vertical extent. There are also two images side-by-side with no text vertically overlapping.
Using HTML this is trivial, I'm using really old, outdated HTML with tables that are aligned left and right as appropriate, and the text simply flows around it.
The attempts I've made with LaTeX appear to be limited, not allowing images to overlap vertically, and insisting that any paragraph can only overlap with at most one image.
I feel like I must be missing something. I know LaTeX and Tex are page formatting systems - I used TeX for my PhD some decades ago - but extensive searching and several weeks of on-and-off hacking about have failed to produce anything cleaner than using \parshape and doing it all "by hand."
All assistance welcome. I'm using vanilla Ubuntu 14.04 (soon to be 18.04) so can use any commands available on that platform, including pdftex and pdflatex, to name just two.
Thanks in advance.

insbox: it defines the\InsertBoxLandInsertBoxRcommands. – Bernard Feb 06 '20 at 18:15insboxcan't vertically overlap the insertions. – Skillmon Feb 06 '20 at 18:58foobar. My previous answer shows how to do the first (at the tex primitive level) doing the second is a lot harder. – David Carlisle Feb 06 '20 at 19:52\parshapeis the tex primitive,insbox,wrapfigetc are layered over that to calculate the required shape, my answer to your last question is the same but withoyt any attempt to hide the actual primitive syntax so it contains a literal sequence of dozens of lengths specifying the shape. insbox wrapfig etc are esssentially just measuring the box then having some loops to calculate that list. Obviously the calculations are easier if there is only one cutout or if they don't overlap but having multiple isn't conceptually harder. ... – David Carlisle Feb 06 '20 at 21:12\parshapehas to be specified before the paragraph, so css style floats where you position images that you encounter mid-paragraph, based on the existing linebreaking are challenging. – David Carlisle Feb 06 '20 at 21:13\placefigurecommand, wiki https://wiki.contextgarden.net/Floating_Objects has some full example code. – Cicada Mar 02 '20 at 10:40floatfltpackage (from 1998) does right and left floats within a paragraph. If the images are small and ornamental, as drop-caps,lettrinepackage may be a design choice; if the images are instructional, marginpars could work, or even better, the wide-marginedtufte-bookclass. Unrelated: The two design choices, windowed-material and typeset-material, allow bi-directional questions: How can I get my PDF to flow like html/css/js? versus How can I get my html/css/js to look like it has been typeset? Would a reader necessarily map one to the other, stylistically? Or look for craft? – Cicada Mar 03 '20 at 11:02Pandoclooks interesting (https://pandoc.org/demos.html); there are many conversion questions (e.g., https://tex.stackexchange.com/questions/1507/how-to-create-pdf-and-html-output-from-the-same-source ). Scanning through those, robust solutions seem to be clustering around the method of a master (I would expect XML) which then 'forks' into Latex->PDF and into (X)HTML/CSS/js – Cicada Mar 03 '20 at 11:33