Recent work on polariton-polariton scattering in semiconductor microcavities under continuous wave excitation conditions is reviewed. For weak non-resonant laser excitation, a marked bottleneck in the polariton distribution is observed, but which is suppressed by polariton-polariton scattering as the laser intensity is increased. However, the high excitation conditions necessary to observe stimulated emission lead to loss of strong coupling and conventional lasing in the weak coupling regime, By contrast for resonant excitation, polaritons are created directly in the polariton trap formed by the microcavity dispersion curve. Stimulated scattering of the bosonic quasi-particles occurs to the emitting state at the centre of the Brillouin zone, and to a companion state at high wavevector. The stimulation phenomena lead to condensation of the bosonic quasi-particles to two specific regions of k-space, and to the formation of a new state with macroscopic coherence. The prospects to achieve a polariton laser under conditions of non-resonant excitation are discussed
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