Most medicinal radionuclides are not naturally occurring and must therefore be produced via nuclear reactions. An understanding of both nuclear reactions and the decay properties of radionuclides can guide the methods for the production of these important tools. Nuclear reactions can be induced with neutrons, charged particles, or photons in both nuclear reactors and particle accelerators. Most therapeutic radionuclides are produced in nuclear reactors that bombard stationary target material with either fast-moving or thermal neutrons produced from fission events, resulting in neutron-rich radionuclides that decay via β-emission. Particle accelerators can produce radionuclides through the bombardment of target materials with charged particles (which can be protons or heavier nuclei) and can produce both β- and α-emitting radionuclides. Another route to therapeutic radionuclides is through the decay of long-lived radionuclides such as 232U, 232Th, and 233U, upon which chemically distinct daughters can be separated for incorporation into radiopharmaceuticals. The rate of the production of a given radionuclide depends on the cross section of the nuclear reaction on the target material, the flux of particles, and the rate of decay of the radionuclide produced. The former property, the cross section, is the probability of the nuclear reaction occurring and is dependent on the type of incident particle, the energy of the incident particle, and the target material. The target material for the nuclear reaction will impact both its initial production and downstream chemistry. Targets must remain stable throughout the irradiation, and the parameters for bombardment must be optimized for both high-purity production and downstream chemistry. The production of high-purity therapeutic radionuclides may involve the use of expensive enriched starting materials that require additional handling for efficient recycling methods. Finally, the production of elementally matched theranostic pairs is of especially high interest due to their identical chemical properties and the identical in vivo behavior of true matched-pair radiopharmaceuticals.