An exciton-polariton is a quasi-particle that emerges from the strong coupling between an exciton and a photon. Recently, the studies of the exciton-polariton have been receiving a great deal of attention in terms of both fundamental physics and potential applications. The very small polariton effective mass and the interactions brought respectively by the photon and excitonic content of polaritons enable a wide range of interesting physical phenomena including the realization of Bose-Einstein condensate, superfluidity, and quantum vortices. In addition to the interest in the basic physics, several device applications of semiconductor microcavities such as polariton switching, bistability, and stochastic resonance have also been proposed. In these researches, the interactions between exciton-polaritons, which is a source of nolinearity, are central. In this thesis, we explore the various aspects of the polariton interactions in semiconductor microcavities. We employ nonlinear spectroscopies as experimental techniques and compare our experimental results with different theoretical models. Firstly, we study lower-lower (upper-upper) polariton self-interactions and lower-upper polariton cross interactions. The self- and crossinteractions are identified in four-wave mixing two-dimensional Fourier spectra, which are followed by theoretical analyses based on a third-order perturbation theory and on a nonperturbative simulation of Gross-Pitaevskii equations. Secondly, using pump-probe spectroscopy, we measure the spin dependent nature of exciton-polariton interactions, which is called spinor interaction. The two spin projections of exciton-polaritons give rise to a spin anisotropy of the polariton interactions. In particular, we show that the polariton interactions with anti-parallel spins presents a scattering resonance behavior via an exciton molecule (biexciton), which we call polaritonic Feshbach resonance. The measurements of the spinor polariton interactions are compared with numerical simulations based on spinor Gross-Pitaevskii equations including the exciton-biexciton coupling. Finally, we explore the decoherence effect induced by the interaction of polaritons. Focusing on the delay dependence of the experimental pump-probe spectra, we find that the excitation induced dephasing (EID) plays an important role in the dynamics of exciton-polaritons. The delay dependence of the pump-probe spectra clearly probes that the coherent and incoherent parts of excitons temporally behave in a different way. These experimental features can be well reproduced only with the excitonic Bloch equations (EBE) approach, which is a theoretical framework that can include the incoherent population of excitons. In the last part of this thesis, a future perspective of the research is discussed while showing preliminary experimental results of pump-probe spectroscopy with a spectrally narrowband pump pulse.