  This paper reviews and extends some recent results on the multivariate
fractional Brownian motion (mfBm) and its increment process. A characterization
of the mfBm through its covariance function is obtained. Similarly, the
correlation and spectral analyses of the increments are investigated. On the
other hand we show that (almost) all mfBm's may be reached as the limit of
partial sums of (super)linear processes. Finally, an algorithm to perfectly
simulate the mfBm is presented and illustrated by some simulations.
