<p>We review some of the interesting consequences that tilts, warps, and eccentricities can introduce into the dynamics, thermodynamics, and observational appearance of accreting systems, with an emphasis on disks around black holes and compact stars. We begin with a review of the two types of precession that are associated with eccentric and tilted orbits in general relativity and Newtonian gravity. We then discuss the types of accretion systems that may manifest tilted or eccentric disks. In separate sections we discuss first tilted and then eccentric disks, each section covering relevant and interesting observational, theoretical, and numerical results. Next, we explore potential connections between the phenomenology of quasi-periodic oscillations and either tilted or eccentric disks. Finally, we present some concluding thoughts and discuss future directions this research might take.</p>