I am interested in open quantum systems, quantum systems that interact with their environment and therefore exhibit a nontrivial interplay between quantum coherence and thermal effects. Understanding how such systems evolve in time and relax toward equilibrium is essential both for fundamental physics and for emerging quantum technologies. Over the years, my group has developed an arsenal of tools to study the dynamics and thermodynamics of such systems. In this talk, I will introduce several key techniques we used to describe open quantum system dynamics. I will then discuss a series of manifestations of anomalous quantum dynamics, including the separation of timescales between local equilibration and global equilibration, long-lived memory of initial conditions and metastable regimes, cooperative effects and delayed relaxation at strong system-bath coupling, and the emergence of the Mpemba effect in thermal state preparation. These examples highlight how coupling to an environment can give rise to rich and sometimes counterintuitive quantum dynamical behavior contrasting conventional notions of relaxation.