 Considering whether space and time are infinite in extent and divisibility has led to many famous puzzles, paradoxes and antimonies. It was on account of such paradoxes that Kant was led to the claim that whether space is finite or infinite escapes any possible empirical determination. Kant’s presentation of the antinomies rested on a number of assumptions (such as the distinction between infinite and unbounded) that were undermined by later results in mathematics or were simply found to be philosophically questionable. Another interesting paradox relates to divisibility. In this section we discuss Kant on the antinomies of space and time and a measure-theoretic solution to this paradox of divisibility. This is followed by a quick overview of some developments in non-Euclidean geometries and relativistic cosmology. In the final part, we mention some recent developments in cosmic topology, an area of cosmology that attempts to determine whether space is finite or infinite by a combination of empirical observation and mathematical theorizing. The emphasis will be on the latter aspect.