Semiconductor microcavities with embedded quantum wells in the strong light-matter coupling regime host quasi-particles called microcavity exciton-polaritons. Their hybrid nature, half-electronic, half-photonic, brings about remarkable nonlinear optical properties. In this work, we focus on microcavities that are structured to enable the coexistence of polaritonic branches with various symmetries and energies. First, a microcavity etched to form micrometers-wide wires is studied. The lateral confinement lifts the degeneracy between the modes which are polarized parallel and orthogonal to the wire direction. We show that this splitting results from built-in constraints which make a precise engineering of the splitting magnitude possible. We then focus on a double microcavity. In the elastic Rayleigh scattering regime, the TE-TM splitting induces a spatial and angular separation of polaritons with different pseudo-spins. We show that this phenomenon, called "Optical Spin Hall Effect", can be controlled by a strong optical pump beam. In the regime of Optical Parametric Oscillation, the light self-organizes to form patterns in the far field. The selection rules for the orientation and polarization of these patterns are explored in the regime of Optical Parametric Amplification. These studies pave the way for the realization of microscopic "lighthouse" devices (able to continuously orientate the light by a simple polarization control) and ultrafast all-optical switches.