The tasks and applications of absolute gravimetry will be outlined. The advances of instrumental development will be shown based on the speaker’s own experience in Ukraine and Germany. This includes different design details of laser ballistic absolute gravimeters and participation in international comparisons. The ERI absolute gravimeter will be presented and first results on development and application of four different digital fringe signal processing methods will be discussed. It is expected to improve performance of that instrument for high-sensitive absolute gravity measurements and reliable study of glacial changes, earthquakes and volcanic activities etc.