The article reviews the detection and certification of entanglement and quantum correlations in condensed matter systems, highlighting recent progress and their significance in both fundamental quantum many-body physics and technological applications. The review covers the theoretical framework, experimental techniques, and practical applications of entanglement witnesses and quantum correlation measures. Key topics include the magnetic susceptibility entanglement witness, one-tangle, concurrence, two-tangle, two-site quantum discord, and quantum coherence measures such as the quantum Fisher information. The review emphasizes the interdisciplinary nature of this research, discussing the challenges and future prospects in areas like correlated electrons, entanglement dynamics, and entangled spectroscopic probes. It also provides a detailed mathematical introduction to entanglement theory and the derivation of experimentally relevant witnesses, making the content accessible to both physicists and researchers in condensed matter physics.The article reviews the detection and certification of entanglement and quantum correlations in condensed matter systems, highlighting recent progress and their significance in both fundamental quantum many-body physics and technological applications. The review covers the theoretical framework, experimental techniques, and practical applications of entanglement witnesses and quantum correlation measures. Key topics include the magnetic susceptibility entanglement witness, one-tangle, concurrence, two-tangle, two-site quantum discord, and quantum coherence measures such as the quantum Fisher information. The review emphasizes the interdisciplinary nature of this research, discussing the challenges and future prospects in areas like correlated electrons, entanglement dynamics, and entangled spectroscopic probes. It also provides a detailed mathematical introduction to entanglement theory and the derivation of experimentally relevant witnesses, making the content accessible to both physicists and researchers in condensed matter physics.