Electromagnetic form factors have long been used to probe the underlying charge and magnetization densities of hadrons and nuclei. Traditional three-dimensional Fourier transform methods are not rigorously applicable for systems with constituents that move relativistically. The use of the transverse charge density is a new, rigorously defined way to analyze electromagnetic form factors of hadrons. This review is concerned with the following issues: what a transverse charge density is, how one is extracted from elastic scattering data, the existing results, its relationship with other observable quantities, and future prospects.
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