The outermost part of the atmosphere of the Sun, the corona, is a unique natural plasma environment where a manifold of extreme and nonlinear phenomena with time scales from a fraction of a second to several years are open to a direct study. Some of these processes, for example coronal mass ejections (CME) and solar flares, are directly linked with the dynamics of magnetohydrodynamic (MHD) waves and oscillations in various coronal plasma non-uniformities. The mechanisms for both the initiation of flares and eruptions by waves and excitation of waves by such impulsive mass and energy releases are considered. This provides us with an important tool for a remote diagnostics of the coronal plasma and physical processes operating there, also known as coronal seismology. In the talk, I will discuss two of such tools which are oscillations of solar quiescent prominences often preceding CME, and quasi-periodic pulsations (QPP) observed in solar flares. The finite-amplitude transverse oscillations of prominences, dense and cool magnetic flux ropes situated in a hot and more rarefied plasma of the solar corona, are modelled through the interaction of the prominence electric current with those in the background plasma. A metastable equilibrium of the prominence and a nonlinear coupling between its horizontal and vertical motions are demonstrated. QPP, repetitive bursts of electromagnetic emission in solar flares, are usually interpreted either in terms of MHD oscillations triggering or modulating the energy releases, or as self-oscillatory regimes of the energy releases. I will discuss mechanisms for generation and damping of QPP by magnetoacoustic waves, based on the effects of their dispersion, potential nonlinearity, and an effective energy exchange between the plasma and the wave.