Where to find info on (polytime) approximability of various discrete optimization problems?

The compendium from Crescenzi is the most complete that I am aware of, despite being pretty old now. You can also watch this more recent (still twelve years old) survey:

Vangelis Paschos. An overview on polynomial approximation of NP-hard problems. https://hal.archives-ouvertes.fr/hal-00186549/document

The following website seems to be no longer maintained, but it is still a useful resource because it covers many problems: http://www.csc.kth.se/~viggo/problemlist/