The defining feature of active matter, self-propulsion requires constant consumption of energy to be maintained. As a result, active matter systems are inherently out of equilibrium and some principles that are accepted as common knowledge, particularly from thermodynamics, do not apply to the active matter systems. Arguably the most popular example is the motility-induced phase separation (MIPS) -- active matter can spontaneously phase separate into liquid-like dense phase and gas-like sparse phase even without any attractive interactions between the self-propelling constituents. In this thesis, I demonstrate the utility of a mechanical perspective in revealing and understanding the underlying physics of seemingly confounding behaviors of active matter systems. In Chapters 2 and 3, I consider the mechanics of a suspension of active colloidal particles when the transport properties (self-propelling speed and diffusivities) vary spatially. The mechanical analysis reveals the reverse-osmotic nature of active matter systems with a spatial variation in activity. I provide an explanation for why physical processes governed by the osmotic pressure of particles can appear in a reversed manner in active matter systems, e.g. a fluid can flow from regions of high concentration to low in a suspension of active colloids. In Chapter 4, I develop a mechanical theory of phase coexistence that applies to both equilibrium and nonequilibrium systems. By applying the mechanical theory to MIPS, I find phase coexistence conditions of the MIPS that allow a construction of a phase diagram, which excellently agrees with the results from computer simulations. The mechanical theory also allows access to the microscopic structure of phase interfaces. By investigating the interfacial structure, I discover interesting nonequilibrium interfacial behavior of the MIPS. I find that the width of the MIPS interface varies nonmonotically with the activity of particles and provide a mechanical explanation for the phenomena
