Vague question is the following: > Is there a classifcation of Lie groupoids? Slightly less vague question is the following: > Is there a (short?) list of "types" of Lie groupoids such that any arbitrary Lie groupoid is Morita equivalent to one from the list? Some Lie groupoids I know are the following: 1. Lie groupoids coming from manifolds $[M\rightrightarrows M]$, 2. Lie groupoids coming from Lie group $[G\rightrightarrows *]$, 3. Lie groupoids coming from action of a Lie group on a manifold $[G\times M\rightrightarrows M]$, 4. Lie groupoids coming from foliation on a manifold $\mathcal{F}(M)$, 5. Lie groupoids coming from a submersion, the submersion groupoid $[M\times_NM\rightrightarrows M]$ 6. Lie groupoids coming from a principal $G$-bundle, the Gauge groupoid, 7. Lie groupoids coming from a vector bundle over $M$, the general linear Lie groupoid $[GL(E)\rightrightarrows M]$. Do we know any "interesting" Lie groupoids that do not belong (not Morita equivalent) to the above list? Only classification I know is if a Lie groupoid is proper and étale, then it is locally looks like action Lie groupoid. I might have forgot one or two types, but these are the only types of Lie groupoids I have come across till now.