  In this paper we present a general framework for Stein's method for
multivariate continuous distributions. The approach gives a collection of Stein
characterisations, among which we highlight score-Stein operators and kernel
Stein operators. Applications include copulas and distance between posterior
distributions. We give a general construction for Stein kernels for elliptical
distributions and discuss Stein kernels in generality, highlighting connections
with Fisher information and mass transport. Finally, a goodness-of-fit test
based on Stein discrepancies is given.
