The creation of carbon and oxygen in our Universe is one of the forefront questions in nuclear astrophysics. The determination of the abundance of these elements is key to our understanding of both the formation of life on Earth and to the life cycles of stars. While nearly all models of different nucleosynthesis environments are affected by the production of carbon and oxygen, a key ingredient, the precise determination of the reaction rate of ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$, has long remained elusive. This is owed to the reaction’s inaccessibility, both experimentally and theoretically. Nuclear theory has struggled to calculate this reaction rate because the cross section is produced through different underlying nuclear mechanisms. Isospin selection rules suppress the $E1$ component of the ground state cross section, creating a unique situation where the $E1$ and $E2$ contributions are of nearly equal amplitudes. Experimentally there have also been great challenges. Measurements have been pushed to the limits of state-of-the-art techniques, often developed for just these measurements. The data have been plagued by uncharacterized uncertainties, often the result of the novel measurement techniques that have made the different results challenging to reconcile. However, the situation has markedly improved in recent years, and the desired level of uncertainty $\approx 10\%$ may be in sight. In this review the current understanding of this critical reaction is summarized. The emphasis is placed primarily on the experimental work and interpretation of the reaction data, but discussions of the theory and astrophysics are also pursued. The main goal is to summarize and clarify the current understanding of the reaction and then point the way forward to an improved determination of the reaction rate.