Systems with massive central objects and multiple smaller orbiters appear in many astrophysical contexts. Their dynamical evolution cannot be described by analytic solutions with finite numbers of terms except for some special cases. In this dissertation, I use semi-analytical methods, N-body simulations, and hydrodynamics simulations to study the dynamical evolution in different kinds of multi-orbiter scenarios: (i) I investigate the outcomes of dynamical instability in planetary systems. I incorporate hydrodynamics effects during planet-planet close encounters into long-term numerical integration, and present the resulting distributions of planetary orbital eccentricities, spins, and obliquities. (ii) I show that, under certain conditions, self-gravitating protoplanetary disks around stars may be prone to a new hydrodynamical instability called eccentric mode instability (EMI). This instability causes disks to develop coherent eccentric patterns spontaneously. I then examine a new way to form rings in disks via EMI, and find a new mechanism to produce highly eccentric exoplanets through a secular resonance between planets and eccentric disks. (iii) I explore the dynamics of stellar-mass black holes (BHs) embedded in gaseous accretion disks around supermassive BHs. I show that these embedded BHs may form long-lived binaries through close encounters due to either gravitational wave emission or gas drag.