The paper reviews various methods for detecting entanglement in quantum systems, focusing on the theory and application of entanglement witnesses. It begins by explaining the basic elements of entanglement theory for two or more particles, including the concepts of pure and mixed states, separability criteria, and bound entanglement. The paper then discusses entanglement verification procedures such as Bell inequalities, entanglement witnesses, and the determination of nonlinear properties of quantum states through measurements on multiple copies. A significant emphasis is placed on the theory and application of entanglement witnesses, which are particularly useful for detecting multipartite entanglement. The paper also covers other entanglement detection methods, including entropic inequalities, estimates of concurrence, and positive maps. Finally, it explores entanglement detection using collective measurements, such as spin squeezing inequalities and optical lattices. The review aims to provide a comprehensive overview of the current state of entanglement detection techniques and their experimental implementations.The paper reviews various methods for detecting entanglement in quantum systems, focusing on the theory and application of entanglement witnesses. It begins by explaining the basic elements of entanglement theory for two or more particles, including the concepts of pure and mixed states, separability criteria, and bound entanglement. The paper then discusses entanglement verification procedures such as Bell inequalities, entanglement witnesses, and the determination of nonlinear properties of quantum states through measurements on multiple copies. A significant emphasis is placed on the theory and application of entanglement witnesses, which are particularly useful for detecting multipartite entanglement. The paper also covers other entanglement detection methods, including entropic inequalities, estimates of concurrence, and positive maps. Finally, it explores entanglement detection using collective measurements, such as spin squeezing inequalities and optical lattices. The review aims to provide a comprehensive overview of the current state of entanglement detection techniques and their experimental implementations.