In this paper we investigate plasma wave electric and magnetic fields in the vicinity of the magnetopause by using recent measurements from the ISEE 1 and 2 spacecraft. Strong electric and magnetic field turbulence is often observed at the magnetopause. The electric field spectrum of this turbulence typically extends over an extremely large frequency range, from less than a few hertz to above 100 kHz, and the magnetic field turbulence typically extends from a few hertz to about 1 kHz. The maximum intensities usually occur in the magnetopause current layer and plasma boundary layer. Somewhat similar turbulence spectra are also sometimes observed in association with flux transfer events and possible 'inclusions' of boundary layer plasma in the magnetosphere. In addition to the broad-band electric and magnetic field turbulence, narrow-band electrostatic emissions are occasionally observed near the electron plasma frequency in the vicinity of the magnetopause. Two possible plasma instabilities, the electrostatic ion-cyclotron instability and the lower-hybrid-drift instability, are considered the primary candidates for explaining the broad-band electric field turbulence. The narrow-band electrostatic emissions near the local electron plasma frequency are believed to be either plasma oscillations or electrostatic waves near the upper-hybrid-resonance frequency.