Again and again I need to look up the logic voltage levels of various logic gate standards like HC, HCT, LVT, and so on. I found a nice article on EETimes: A brief recap of popular logic standards. The page has a picture that recaps all the popular standards along with their Voh, Vih, Vil, and Vol voltage levels. However, the picture resolution is very low quality, and it is also not evident at the first glance what is the relation between standards. So I redraw the picture in Inkscape, an open-source SVG editor. The result is here (click to see large image):
As usual, Voh is the minimal voltage of logic-1 on output, Vol is the maximal voltage of logic-0 on output, Vih is the minimal voltage of logic-1 on input, and Vil is the maximal voltage of logic-0 on input.
Two gates of voltage standards (1) and (2) are compatible in the 1->2 direction if Voh(1) > Vih(2) and Vol(1) < Vil(2).
All the 5V and 3.3V standards except HC, AHC, and AC are compatible in any direction, if the 3.3V gates are 5V-tolerant. The HC, AHC, and AC gates are CMOS technology, having rather high Vih=3.5V compared to original TTL with Vih=2.0V. The ‘T’ series–ACT, HCT, AHCT–was created to interface 5V CMOS with the original 5V TTL. It has CMOS-compatible output levels (that are also compatible with TTL), and TTL-compatible inputs with Vih=2.0V.