Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations protected by topology and symmetry. They are analogous to graphene and have connections to relativistic chiral fermions and solid-state topological insulators. These materials exhibit protected surface states and unique responses to electric and magnetic fields. Theoretical foundations, proposed realizations, experimental results, and their relation to other states of matter are reviewed. Weyl semimetals have Weyl nodes, which are sources and sinks of Berry flux, leading to Fermi arc surface states and the chiral anomaly. Dirac semimetals have Dirac points, which are protected by symmetry and lead to similar phenomena. The topological properties of these materials are studied through their band structures, transport properties, and interactions with magnetic fields. The review also discusses related states of matter, such as topological line nodes, nodal superconductors, and quadratic band touchings. The study of Weyl and Dirac semimetals has led to the discovery of new materials and insights into topological phases of matter.Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations protected by topology and symmetry. They are analogous to graphene and have connections to relativistic chiral fermions and solid-state topological insulators. These materials exhibit protected surface states and unique responses to electric and magnetic fields. Theoretical foundations, proposed realizations, experimental results, and their relation to other states of matter are reviewed. Weyl semimetals have Weyl nodes, which are sources and sinks of Berry flux, leading to Fermi arc surface states and the chiral anomaly. Dirac semimetals have Dirac points, which are protected by symmetry and lead to similar phenomena. The topological properties of these materials are studied through their band structures, transport properties, and interactions with magnetic fields. The review also discusses related states of matter, such as topological line nodes, nodal superconductors, and quadratic band touchings. The study of Weyl and Dirac semimetals has led to the discovery of new materials and insights into topological phases of matter.