  We discuss two generalizations of Lie groupoids. One consists of Lie
$n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$.
The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a
differentiable stack. We build a 1-1 correspondence between Lie 2-groupoids and
stacky Lie groupoids up to a certain Morita equivalence. We prove this in a
general set-up so that the statement is valid in both differential and
topological categories. \Equivalences of higher groupoids in various categories
are also described.
