The gravity anomalies are an important tool in the hands of the geodesists and geophysicists. For instance, the positive Bouguer anomalies of the oceans and the negative ones of the mountains show qualitatively that isostatic equilibrium exists in broad lines. The isostatic anomalies are even able to localize the isostatically compensating layers and in such a way to determine the thickness of the Earth's crust. Also local disturbing masses of different types are not too difficult to discover. With the rapid and accurate gravimeters beginning a new epoch in gravimetry, quite new views for detailed geophysical study of the behavior of the Earth's interior are to be presented. But the gravity anomalies must be used carefully. In some cases they too easily lead us to wrong conclusions.