We review research on geomagnetic pulsations carried out using magnetic field measurements from the CHAMP low-Earth-orbit (LEO) satellite and ground-based stations in South Africa and Hungary. The high quality magnetic field measurements from CHAMP made it possible to extract and clearly resolve Pi2 and Pc3 pulsations in LEO satellite data. Our analyses for nighttime Pi2 pulsations are indicative of a cavity mode resonance. However, observations of daytime Pi2 pulsation events identified in ground station data show no convincing evidence of their occurrence in CHAMP data. We also studied low-latitude Pc3 pulsations and found that different types of field line resonant structure occur, namely discrete frequencies driven by a narrow band source and L-dependent frequencies driven by a broad band source.