I will discuss the notion of a lattice in a locally compact quantum group that is meant to mimic its classical analogue. For locally compact groups, at least part of the interest stems from the fact that property (T) transfers between such groups and their lattices. I will discuss similar "permanence" properties for quantum lattices, as well as issues related to characterizing invariant measures on homogeneous spaces of locally compact quantum groups. (Joint with Michael Brannan and Ami Viselter.)