Property-testers are fast randomized algorithms for distinguishing
between graphs (and other combinatorial structures) satisfying a
certain property, from those that are far from satisfying it. In
many cases one can design property-testers whose running time is in
fact {\em independent} of the size of the input. In this paper we
survey some recent results on testing graph properties. A common
thread in all the results surveyed is that they rely heavily on the
simple yet useful notion of graph homomorphism. We mainly focus
on the combinatorial aspects of property-testing.