The article reviews the properties, theoretical foundations, and experimental progress of Weyl and Dirac semimetals in three-dimensional (3D) solids. These materials are characterized by gapless electronic excitations protected by topology and symmetry, similar to graphene but with more complex topological features. The review covers the historical context, including the development of relativistic wave equations and the discovery of Weyl and Dirac fermions, and their relevance in condensed matter physics. It discusses the conditions for the formation of Weyl and Dirac nodes in band structures, the topological invariants associated with these nodes, and the resulting surface states and novel responses to electric and magnetic fields. The article also explores the experimental identification of Weyl and Dirac systems, the transport properties, and the connection to other states of matter, such as topological insulators and superconductors. Finally, it highlights the potential of Weyl semimetals as platforms for testing relativistic theories and exploring new fermion types not found in high-energy physics.The article reviews the properties, theoretical foundations, and experimental progress of Weyl and Dirac semimetals in three-dimensional (3D) solids. These materials are characterized by gapless electronic excitations protected by topology and symmetry, similar to graphene but with more complex topological features. The review covers the historical context, including the development of relativistic wave equations and the discovery of Weyl and Dirac fermions, and their relevance in condensed matter physics. It discusses the conditions for the formation of Weyl and Dirac nodes in band structures, the topological invariants associated with these nodes, and the resulting surface states and novel responses to electric and magnetic fields. The article also explores the experimental identification of Weyl and Dirac systems, the transport properties, and the connection to other states of matter, such as topological insulators and superconductors. Finally, it highlights the potential of Weyl semimetals as platforms for testing relativistic theories and exploring new fermion types not found in high-energy physics.