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
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.