  In the paper we consider Lamperti type theorems for random fields. Together
with known results we present some new results on ${\mathbb R}^m$-valued
self-similar fields $\{{\bf X} ({\bf t}), \ {\bf t} \in {\mathbb R}^d \}$,
their domains of attraction and the so-called Lamperti transformations,
expressing the relation between self-similarity and stationarity. Also we
investigate regularly and slowly varying functions of several variables.
