Exciton-polaritons are quasiparticles that are found in semiconductor microcavities and are composed of quantum well excitons strongly coupled to cavity photons. Being composite bosons polaritons can undergo a condensation process, similar to Bose-Einstein condensation. Theoretically, in many aspects the dynamics of polariton condensates can be described by a Gross-Pitaevskii (GP) equation. The main aim of this thesis is to theoretically investigate the dynamics of polariton condensates in semiconductor microcavities under nonresonant (incoherent) excitation. First, in uniform semiconductor microcavities, modulational instability, spiraling waves, and vortices of condensates are studied under homogeneous excitation. Under localized ring-shaped pumps, crater-shaped vortices are found, while their rotation directions, the signs of topological charges, are uncertain due to noisy initial conditions. Two simpler methods are introduced for the vortex control: elliptical pump control and vortex-vortex control. Second, in nonuniform semiconductor microcavities with periodic potentials, a clear band-gap structure is observed. In weak-contrast lattices a simplified model, which has very good agreement with the full GP model, is developed. In tight-trapping lattices, collective state transitions of condensates are studied under narrow pumps. Last, besides the dynamics of condensates in the scalar model, the dynamics of condensates in the spinor model are also studied considering the polarization effect. It is shown that the interplay of two nonlinearities supports stable symbiotic solitons and vortices.