Exciton-polaritons are half-light half-matter bosonic quasiparticles formed by the strong coupling between quantum well excitons and the photonic mode of a planar semiconductor microcavity. By increasing the polariton population above a threshold density, polaritons can macroscopically occupy the ground state of the dispersion and form a non-equilibrium Bose-Einstein condensate. This thesis addresses some of the fundamental concepts studied in polariton microcavities, such as dark solitons, polariton spin textures and condensation, by concentrating on the linear and nonlinear nature of these effects. In the first part, the formation of dark solitons is studied by investigating the propagation and scattering of polaritons in a planar microcavity in the linear regime. The propagation of the polariton wave across an extended defect creates phase and intensity patterns with identical qualitative features previously attributed to dark and half-dark solitons of polaritons. By combining both experimental evidence and theoretical analysis, all the experimental observations supporting the formation of dark solitons in polariton microcavities are questioned. Since they are observed with negligible nonlinearity (i.e., polariton-polariton interaction), they are not sufficient to identify dark and half-dark solitons. A condition based on the healing length of the condensate is proposed as a new criterion to identify dark solitons in polariton microcavities. In the second part, the spin dynamics of polariton condensates is investigated in the non-linear emission regime, by studying the spatial, angular, energy and transient dynamics of the polariton emission. In a radially expanding condensate, polaritons with opposite spin arrange themselves in geometrically ordered spin textures and propagate over hundreds of microns in the plane of the microcavity. Depending on the polarization of the excitation pump different spin textures are observed. Moreover, a polariton \spin whirl" namely a spin texture that rotates in the plane of the microcavity on picosecond scale is reported for the first time. Finally, the condensation of polaritons in a strain compensated microcavity is investigated. Signatures of polariton condensation, according to the current understanding of polariton condensates, are experimentally observed, including the observation of a second threshold which marks the transition from the strong to the weak-coupling regime.