Why do we see shadows in the following black-and-white optical illusion?
Looks like these are variations on the Hermann grid illusion, wiki page here: https://en.wikipedia.org/wiki/Grid_illusion

As the wiki page notes, the first-pass explanation of this was lateral inhibition, but this is not really 100% satisfactory. 
There's a nice quick walk-through of the old explanation and the problems with it here: http://web.mit.edu/bcs/schillerlab/research/A-Vision/A15-2.htm 
A journal paper version of this stuff from the same lab is:
Schiller, P. H., &amp; Carvey, C. E. (2005). The Hermann grid illusion revisited. Perception, 34(11), 1375-1397.