The three-body problem describes the motion of three objects under the influence of their mutual gravity. It is one of the oldest problems in astrophysics. No closed form analytical solution is possible to the general three body problem due to its chaotic nature. Despite its rich history, the three-body problem remains an active area of research. Recent advancements in the field are motivated by new discoveries pertaining to exoplanets and blackholes. In this work we focus on resonant and secular interactions in three body systems, with a goal to understand how these interactions influence the long- term stability and evolution of three body systems. We apply our theoretical investigations of these physical processes to a wide range of observed systems. We find that secular and resonant perturbations can significantly affect the stability limit of mutually inclined planets. Planets in retrograde configurations are much more stable than prograde configurations, with secular perturbations significantly destabilizing the system when 20° < $I_mut$ < 160°. In addition, we find that secular three body dynamics can also help us constrain the inclination of the hypothetical Planet-9 in the outer solar system, and explain the observed retrograde stellar obliquities of hot Jupiters. We also propose a novel pathway through which compact binaries could merge due to eccentricity excitation caused by resonant interactions induced by a massive coplanar companion. Specifically, a compact binary migrating in an AGN disk could be captured in a precession-induced resonance, when the apsidial and nodal precession rates of the binary are commensurable to the orbital period around the supermassive black hole. Eccentricity is excited when the binary sweeps through the resonance which happens only when it migrates on a timescale 10-100 times the libration timescale of the resonance. The eccentricity excitation of the binary can reduce the merger timescale by a factor up to $10^3-10^5$.