Abstract: Active matter is a novel class of nonequilibrium systems composed of autonomous constituents， which can consume locally stored free energy to achieve selfpropelled motion. Examples of active matter can be found at diverse length scales，from animal groups to cell colonies and tissues to in vitro cytoskeletal extracts and manmade microscopic motors. Energy input at the level of the individual constituents drives active matter systems out of thermal equilibrium and leads to a wide range of collective phenomena. Here，we review， from both theoretical and experimental perspectives，some of these intriguing phenomena in active matter，including collective migration，spontaneous flow，motile topological defects and various phase transitions. Applications of active matter research in biology，mathematics， and engineering will also be discussed.