Despite various shortcomings, the earthquake magnitude scale is one of the most fundamental earthquake source parameters to be used for catalogs. Although use of a uniform scale is desirable, it is not always possible because of changes in instrumentation, the data reduction method and the magnitude formula, the station distribution, etc. As a result, various magnitude scales have been developed and are currently in use. Recent developments in seismometry and earthquake source theories provide more quantitative source parameters than the magnitude. In order to maintain continuity and uniformity of the data, it is important to relate these magnitude scales and the new parameters. In view of this importance, relations between different magnitude scales are examined with an emphasis on the difference in the period of the waves used for the magnitude determination. Use of several magnitude scales determined at different periods provides a convenient method for characterizing earthquakes. The moment magnitude can be used to quantify both shallow and deep earthquakes on the basis of wave energy radiated, and provides a uniform scheme.