It has become commonplace to record high-resolution marine seismic profiles in digital format and to base the choice of sampling rate on the traditional assumption that seismic signals are of limited bandwidth. The truth is that seismic signals are causal and the Heisenberg uncertainty principle prohibits causal signals being bandlimited. Since only signals with finite bandwidth can be digitized without loss of information, the implication is that at least some resolution is always lost when seismic signals are digitized. A research program to improve seismic resolution, begun in 1987 at the University of Utrecht and now continuing at the University of Mississippi, has investigated ways to minimize that loss and to recover from seismograms as much geologic information as possible. This paper addresses theoretical considerations encountered by the program and presents experimental results which demonstrate the seismic resolution it is currently possible to achieve in shallow and deep water using commercially available systems.