This dissertation aims to investigate systems in which several optical and mechanical degrees of freedom are coupled through optomechanical interactions. Multimode optomechanics creates the prospect of integrated functional devices and it allows us to explore new types of optomechanical interactions which account for collective dynamics and optically mediated mechanical interactions. Owing to the development of fabrication techniques for micro- and nano-sized mechanical elements, macroscopic mechanical oscillators can be cooled to the deep quantum regime via optomechanical interaction. Based on the possibility to control the motion of mechanical oscillators at the quantum level, we design several schemes involving mechanical systems of macroscopic length and mass scales and we explore the nonlinear dynamics of mechanical oscillators. The first scheme includes a quantum cantilever coupled to a classical tuning fork via magnetic dipole-dipole interaction and also coupled to a single optical field mode via optomechanical interaction. We investigate the generation of nonclassical squeezed states in the quantum cantilever and their detection by transferring them to the optical field. The second scheme involves a quantum membrane coupled to two optical modes via optomechanical interaction. We explore dynamic stabilization of an unstable position of a quantum mechanical oscillator via modulation of the optical fields. We then develop a general formalism to fully describe cavity mediated mechanical interactions. We explore a rather general configuration in which multiple mechanical oscillators interact with a single cavity field mode. We specifically consider the situation in which the cavity dissipation is the dominant source of damping so that the cavity field follows the dynamics of the mechanical modes. In particular, we study two limiting regimes with specific applications: the weak-coupling regime and single-photon strong-coupling regime. In the weak-coupling regime, we build a protocol for quantum state transfer between mechanical modes. In the single-photon coupling regime, we investigate the nonlinear nature of the mechanical system which generates bistability and bifurcation in the classical analysis and we also explore how these features manifest themselves in interference, entanglement, and correlation in the quantum theory.