This article reviews the physics of locomotion in microswimmers, both biological and synthetic, and their collective behavior. It begins by discussing the essential role of locomotion in microorganisms, such as bacteria and sperm, for various activities like searching for food, orientation, and reproduction. The dynamics of microswimmers at low Reynolds numbers, where fluid friction dominates over inertia, are highlighted, emphasizing the evolution of propulsion mechanisms like rotating helical flagella and snake-like motion of eukaryotic flagella. The article then delves into the hydrodynamics of swimming, including the solution of Stokes equations, the behavior of dipole swimmers, and the effects of fluctuations and noise. It explores the synchronization of flagella and cilia, as well as swimming near surfaces. The collective behavior of microswimmers, including isotropic and anisotropic swimmers, is discussed, along with the emergence of complex patterns and vortices. Finally, the article examines other forms of active matter, such as mixtures of filaments and motor proteins, and cellular tissues, providing a comprehensive overview of the physics of microswimmers and their collective phenomena.This article reviews the physics of locomotion in microswimmers, both biological and synthetic, and their collective behavior. It begins by discussing the essential role of locomotion in microorganisms, such as bacteria and sperm, for various activities like searching for food, orientation, and reproduction. The dynamics of microswimmers at low Reynolds numbers, where fluid friction dominates over inertia, are highlighted, emphasizing the evolution of propulsion mechanisms like rotating helical flagella and snake-like motion of eukaryotic flagella. The article then delves into the hydrodynamics of swimming, including the solution of Stokes equations, the behavior of dipole swimmers, and the effects of fluctuations and noise. It explores the synchronization of flagella and cilia, as well as swimming near surfaces. The collective behavior of microswimmers, including isotropic and anisotropic swimmers, is discussed, along with the emergence of complex patterns and vortices. Finally, the article examines other forms of active matter, such as mixtures of filaments and motor proteins, and cellular tissues, providing a comprehensive overview of the physics of microswimmers and their collective phenomena.