This study is concerned with the measurement and interpretation of magnetic hyperfine anomalies in electronic and muonic atoms. i.e. effects of the distribution of nuclear magnetization on the magnetic dipole hyperfine interaction. After a summary of the relevant theory and a review of experimental techniques, hyperfine anomaly results are discussed in terms of various nuclear models. The use of the anomaly for yielding information about the origin of magnetic hyperfine interactions is outlined. Experimental and theoretical hyperfine anomalies are tabulated.