The long range nature of gravity complicates the dynamics of self-gravitating many-body systems such as galaxies and dark matter (DM) halos. Relaxation/equilibration of perturbed galaxies and cold dark matter halos is typically a collective, collisionless process, and depends on the perturbation timescale (impulsive, resonant or adiabatic). First, I shall briefly discuss a non-perturbative treatment of impulsive encounters between galaxies or halos. Next, I shall present a linear perturbative formalism to compute the response of disk galaxies to perturbations of diverse spatiotemporal characteristics (bars, satellite impacts, etc.). I shall elucidate how phase-mixing of the disk response gives rise to phase-space spirals akin to those observed by Gaia in the Milky Way disk, and how these features can be used to constrain the dynamical history and DM distribution of our galaxy. Finally, I shall present two novel techniques to model the secular evolution (dynamical friction) of a massive perturber on a circular orbit in a spherical host galaxy/halo due to resonant interactions with the field particles: 1. a self-consistent, time-dependent, perturbative treatment and 2. a non-perturbative orbit-based framework. These two approaches explain the origin of certain dynamical phenomena (unexplained in the standard Chandrasekhar and LBK formalisms) observed in N-body simulations of cored galaxies: core-stalling, the apparent cessation of dynamical friction driven infall of a massive perturber in a constant density core, and dynamical buoyancy, an enhancing torque that pushes out the perturber from inside the core region. I shall briefly discuss the astrophysical implications of core-stalling and buoyancy, e.g., supermassive black hole mergers, constraining the inner density profile (core vs cusp) of DM dominated dwarf galaxies and the DM particle nature, and so on.