The ability of accelerator mass spectrometry (AMS) to measure very small concentrations of the nuclides 10Be, 14C, 26Al, 36Cl, and 129I has led to many innovative applications in geologic research. To take advantage of this opportunity in the geosciences, it is important to understand how AMS works, how these nuclides are produced, and how they can be applied to geologic problems. We first discuss the basics of AMS, explaining what gives the method its ability to count small numbers of these nuclides. We review how these nuclides are produced and transported in the atmosphere, hydrosphere, and lithosphere. We then explain the ways that AMS is being used to solve a wide range of problems in geologic research by discussing specific applications in areas such as geomorphology, tectonics, climatology, hydrology, and geochronology.