Microcavity exciton-polaritons are half-matter half-light quasiparticles with outstanding properties. This offers a great way to access and control fundamental excitations in a solid by simple optical means. Therefore, apart from their importance in fundamental physical research, microcavity polaritons play an important role in various application proposals in the field of all-optical and quantum computing. This thesis is dedicated to the study of confined zero-dimensional microcavity exciton-polaritons. Confinement in all three dimensions is obtained in our case through shallow optical traps created by small local elevations on top of the spacer layer of a planar microcavity sample. This results in a discrete spectrum of confined polariton states, which co-exist with the two-dimensional polaritons in the planar region of the sample. First we investigate the confined polariton states through resonant continuous wave optical excitation. We demonstrate different ways to manipulate the wave function of the trapped zero-dimensional polaritons by optical means. The experimental results are explained and reproduced in the frame of a theoretical model based on the Gross-Pitaevskii equations. Essential for the manipulation is a phase locking effect which locks the phase of the coherent polariton state to the phase of the laser at the excitation point in the reciprocal space. We investigate as well the spatial dynamics of confined polaritons after resonant optical excitation. The experiments are performed in the linear, as well as in the nonlinear regime. In the linear regime, when exciting a small number of well separated states, the observed dynamics are explained in terms of interference between the excited states. In the case where the energy separation becomes equal or smaller than the linewidth of the confined states, the observed dynamics are better explained in terms of ballistically propagating two-dimensional polaritons. In the nonlinear regime we evidence the role of the energy blue shift and parametric scattering on the spatial dynamics. We evidence as well a spin anisotropy of the nonlinear polariton interactions. Further we show how the nonlinear and anisotropic polariton interactions give rise to a spin dependent bistability in our system of confined polaritons. Based on this bistability we demonstrate an all-optical spin flip-flop with outstanding performance. The results are explained with a theoretical model, which shows that the flip-flop operations are based on nonlinear losses between the spin-up and spin-down polariton population. The demonstrated operation could lead to the creation of polariton based high speed all-optical RAM devices for optical computing.