This paper presents a comprehensive review of dispersive Alfven waves in sp
ace and laboratory plasmas. We start with linear properties of Alfven waves
and show how the inclusion of ion gyroradius, parallel electron inertia, a
nd finite frequency effects modify the Alfven wave properties. Detailed dis
cussions of inertial and kinetic Alfven waves and their polarizations as we
ll as their relations to drift Alfven waves are presented. Up to date obser
vations of waves and field parameters deduced from the measurements by Frej
a, Fast, and other spacecraft are summarized. We also present laboratory me
asurements of dispersive Alfven waves, that are of most interest to auroral
physics. Electron acceleration by Alfven waves and possible connections of
dispersive Alfven waves with ionospheric-magnetospheric resonator and glob
al field-line resonances are also reviewed. Theoretical efforts are directe
d on studies of Alfven resonance cones, generation of dispersive Alfven wav
es, as well their nonlinear interactions with the background plasma and sel
f-interaction. Such topics as the dispersive Alfven wave ponderomotive forc
e, density cavitation, wave modulation/filamentation, and Alfven wave self-
focusing are reviewed. The nonlinear dispersive Alfven wave studies also in
clude the formation of vortices and their dynamics as well as chaos in Alfv
en wave turbulence. Finally, we present a rigorous evaluation of theoretica
l and experimental investigations and point out applications and future per
spectives of auroral Alfven wave physics.