The paper discusses the development of the moment magnitude scale (Mw) and its relationship with other earthquake magnitude scales. It explains that the nearly coincident relations between seismic moment M0 and magnitudes ML, Mθ, and Mw imply a moment magnitude scale. The formula M = 1/2 log M0 - 10.7 is valid for a range of magnitudes. The paper also notes that traditional magnitude scales like ML, Ms, and mb are bounded due to limitations in instrumentation and source characteristics. Hanks [1979] demonstrated that the maximum reported mb ≈ 7 and Ms ≈ 8.3 can be explained by these limitations. The paper also discusses the saturation of these scales at high magnitudes and the development of Mw based on radiated energy, which avoids saturation. Kanamori [1977] derived Mw using the relation between radiated energy Es and seismic moment M0, leading to the formula log M0 = 1.5Mw + 16.1. This formula is consistent with empirical relations for other magnitudes. The paper presents data on several earthquakes, showing good agreement between ML, Ms, and Mw for most events, with exceptions due to saturation or high stress drop. The paper also discusses the upper limits of earthquake magnitudes for California earthquakes, suggesting an upper limit of M ≈ 8.0. The paper concludes that the moment magnitude scale is a reliable measure of earthquake size, avoiding the saturation issues of other scales.The paper discusses the development of the moment magnitude scale (Mw) and its relationship with other earthquake magnitude scales. It explains that the nearly coincident relations between seismic moment M0 and magnitudes ML, Mθ, and Mw imply a moment magnitude scale. The formula M = 1/2 log M0 - 10.7 is valid for a range of magnitudes. The paper also notes that traditional magnitude scales like ML, Ms, and mb are bounded due to limitations in instrumentation and source characteristics. Hanks [1979] demonstrated that the maximum reported mb ≈ 7 and Ms ≈ 8.3 can be explained by these limitations. The paper also discusses the saturation of these scales at high magnitudes and the development of Mw based on radiated energy, which avoids saturation. Kanamori [1977] derived Mw using the relation between radiated energy Es and seismic moment M0, leading to the formula log M0 = 1.5Mw + 16.1. This formula is consistent with empirical relations for other magnitudes. The paper presents data on several earthquakes, showing good agreement between ML, Ms, and Mw for most events, with exceptions due to saturation or high stress drop. The paper also discusses the upper limits of earthquake magnitudes for California earthquakes, suggesting an upper limit of M ≈ 8.0. The paper concludes that the moment magnitude scale is a reliable measure of earthquake size, avoiding the saturation issues of other scales.