Entanglement detection is a crucial aspect of quantum information theory, aiming to determine whether a given quantum state is entangled. This paper reviews various methods for detecting entanglement, including Bell inequalities, entanglement witnesses, and spin squeezing inequalities. It emphasizes the theory and application of entanglement witnesses, which are widely used tools for detecting entanglement. The paper also discusses several experiments where these methods have been implemented. The paper begins with an introduction to entanglement theory, covering bipartite and multipartite entanglement. It explains the concepts of separability and entanglement for both pure and mixed states, and introduces various separability criteria, such as the PPT criterion and the CCNR criterion. These criteria are used to determine whether a state is separable or entangled. The paper then discusses multipartite entanglement, including different classes of entangled states and their properties. It also covers entanglement measures and their applications in quantum information theory. The paper reviews Bell inequalities as a tool for verifying entanglement, explaining how violations of Bell inequalities indicate quantum entanglement. It also discusses entanglement witnesses, which are used to detect entanglement in quantum states. The paper further explores other methods for entanglement detection, such as entropic inequalities, variance-based criteria, and nonlinear entanglement witnesses. It also discusses entanglement detection with collective measurements, including spin squeezing inequalities and optical lattices. The paper concludes with a summary of the key findings and the importance of entanglement detection in quantum information theory.Entanglement detection is a crucial aspect of quantum information theory, aiming to determine whether a given quantum state is entangled. This paper reviews various methods for detecting entanglement, including Bell inequalities, entanglement witnesses, and spin squeezing inequalities. It emphasizes the theory and application of entanglement witnesses, which are widely used tools for detecting entanglement. The paper also discusses several experiments where these methods have been implemented. The paper begins with an introduction to entanglement theory, covering bipartite and multipartite entanglement. It explains the concepts of separability and entanglement for both pure and mixed states, and introduces various separability criteria, such as the PPT criterion and the CCNR criterion. These criteria are used to determine whether a state is separable or entangled. The paper then discusses multipartite entanglement, including different classes of entangled states and their properties. It also covers entanglement measures and their applications in quantum information theory. The paper reviews Bell inequalities as a tool for verifying entanglement, explaining how violations of Bell inequalities indicate quantum entanglement. It also discusses entanglement witnesses, which are used to detect entanglement in quantum states. The paper further explores other methods for entanglement detection, such as entropic inequalities, variance-based criteria, and nonlinear entanglement witnesses. It also discusses entanglement detection with collective measurements, including spin squeezing inequalities and optical lattices. The paper concludes with a summary of the key findings and the importance of entanglement detection in quantum information theory.