This article presents an overview of plasma wave observations in Geospace by the Plasma Wave Instrument (PWI) onboard the GEOTAIL spacecraft. The GEOTAIL spacecraft covers a wide area in Geospace from the solar wind down to the distant geomagnetic tail. Accordingly the plasma wave data obtained in the vast area show a very rich collection of plasma waves and related phenomena. To overview and understand the GEOTAIL plasma wave data, this article covers not only the plasma wave data themselves, but also the details of the PWI instrument and related computer experiments. The plasma wave data are discussed from two aspects: from the wave modes and related wave-particle and wave-wave interactions, and from their geophysical roles in the different regions of Geospace.