In this talk, we present some recent results on statistical and sample path properties of several classes of multivariate Gaussian random fields including multivariate Mat’ern Gaussian fields, operator fractional Brownian motion, vector-valued operator-scaling random fields, and matrix-valued Gaussian random fields. These results illustrate explicitly the effects of the dependence structures among the coordinate processes on statistical and sample path properties of multivariate Gaussian random fields. A useful technical tool for establishing these results is the property of strong local nondeterminism.