Recent satellite-based observations of oceanic planetary waves have improved our knowledge of the wave properties and lead to advancements in the theory. Firstly, we review some of the techniques adopted to extract the information on planetary wave properties, illustrating them with examples based on satellite altimeter data, and we summarize the main findings. Then we discuss a cross-spectral approach for the comparison of the wave signals in the different datasets (altimetry, ocean colour and sea surface temperature) that is necessary to unveil the causes of the newly found wave signature in satellite-derived maps of phytoplankton chlorophyll, a discovery that is attracting considerable interest as it implies some effects of the waves on biology