Over the last 60 years, our understanding of how cosmic rays produce cosmogenic nuclides has grown from basic physical considerations. We introduce the different types of cosmic ray particles and how their flux varies with altitude, latitude, and time. Accurately describing these variations remains a challenge for some regions when calculating production rates. We describe current and emerging computational methods for calculating production rates that address this challenge. Continuing developments in our understanding of modern and prehistoric cosmic ray fluxes and energy spectra in Earth's atmosphere and at its surface are bound to contribute in the future to more robust applications.