Ion transport in crystalline fast ionic conductors is a complex physical phenomenon. Certain ionic species (e.g., Ag+, Cu+, Li+, F-, O-2(-), H+) in a solid crystalline framework can move as fast as in liquids. This property, although only observed in a limited number of materials, is a key enabler for a broad range of technologies, including batteries, fuel cells, and sensors. However, the mechanisms of ion transport in the crystal lattice of fast ionic conductors are still not fully understood despite the substantial progress achieved in the last 40 years, partly because of the wide range of length and time scales involved in the complex migration processes of ions in solids. Without a comprehensive understanding of these ion transport mechanisms, the rational design of new fast ionic conductors is not possible. In this review, we cover classical and emerging characterization techniques (both experimental and computational) that can be used to investigate ion transport processes in bulk crystalline inorganic materials which exhibit predominant ion conduction (i.e., negligible electronic conductivity) with a primary focus on literature published after 2000 and critically assess their strengths and limitations. Together with an overview of recent understanding, we highlight the need for a combined experimental and computational approach to study ion transport in solids of desired time and length scales and for precise measurements of physical parameters related to ion transport.