This article reviews recent progress in applying nonequilibrium statistical mechanics and hydrodynamics to understand the behavior of active matter, which consists of particles with internal degrees of freedom that can take in and dissipate energy, leading to systematic movement. The review covers a wide range of active systems, including living organisms and their motile constituents, and presents a unified view that encompasses both biological and inanimate analogues. The focus is on the collective behavior of systems with a large number of constituents, using the tools of condensed matter and statistical physics. Key topics include the mechanics of flocks, the cytoskeleton, and the instability of orientationally ordered active suspensions. The review also discusses the implications of active processes on viscosity and the enhancement of biological noise. Experimental and theoretical efforts are discussed side by side, highlighting the progress and challenges in this rapidly evolving field.This article reviews recent progress in applying nonequilibrium statistical mechanics and hydrodynamics to understand the behavior of active matter, which consists of particles with internal degrees of freedom that can take in and dissipate energy, leading to systematic movement. The review covers a wide range of active systems, including living organisms and their motile constituents, and presents a unified view that encompasses both biological and inanimate analogues. The focus is on the collective behavior of systems with a large number of constituents, using the tools of condensed matter and statistical physics. Key topics include the mechanics of flocks, the cytoskeleton, and the instability of orientationally ordered active suspensions. The review also discusses the implications of active processes on viscosity and the enhancement of biological noise. Experimental and theoretical efforts are discussed side by side, highlighting the progress and challenges in this rapidly evolving field.