Living systems maintain their structures and functions by staying far from equilibrium, which they achieve by taking and dissipating energy without any external bias. Active matter, which autonomously converts stored or ambient energy into systematic motion, provides a natural framework for studying the physics of such systems. Unlike the conventional nonequilibrium systems driven by boundary reservoirs or global external fields, active matter is driven out of equilibrium at the level of each particle, which leads to a plethora of novel collective behaviors. In this talk, I will focus on three major aspects of such phenomena: fluxes induced by spatial asymmetries, phase separation even in the absence of attractions, and spontaneous emergence of orientational order with anomalous fluctuations. I will demonstrate how one can utilize recent theoretical advancements of statistical physics to study these phenomena and discuss their biological implications.