Semiconductor microcavities have attracted much recent interest because they utilize simultaneously 2D confinement of both excitons and photons in the same heterostructure. Strong coupling of these two states produces unique dynamics that can be well described in a quasiparticle state, the cavity polaritons. Their dispersion relation is dramatically modified with an apparent trap in k-space offering exciting new possibilities for tailoring nonlinear optical properties in microcavities. The reduced density of states inside the trap allows the macroscopic occupancy of polaritons producing much of the new physics. This paper describes recent work on nonlinear effects in semiconductor microcavities including stimulated scattering, parametric oscillation and non-equilibrium phase transition. By teaching polaritons new tricks, both fundamental questions about their bosonic nature can be answered and practical applications in a variety of optoelectronic and interferometric devices can be found.