TITLE: Limits in span categories
QUESTION [5 upvotes]: What are the limits in the span categories? and what is known about them in the literature?

REPLY [3 votes]: I can think of two interesting classes of limits in bicategories of spans (which, as Urs mentioned, are necessarily also colimits, since $\mathrm{Span}(C)$ is equivalent to its opposite).
The first is a generalization of Urs's comment: any van Kampen colimit in $C$ is a (co)limit in $\mathrm{Span}(C)$ — and conversely, this property characterizes van Kampen colimits.  This is in 

Pawel Sobocinski and Tobias Heindel, Being Van Kampen is a universal property, arXiv:1101.4594

The second is that $\mathrm{Span}(C)$ always has Eilenberg-Moore objects for comonads (a sort of 2-categorical limit) — and this figures in a characterization of bicategories of the form $\mathrm{Span}(C)$.  This is in

Stephen Lack, R.F.C. Walters, and R.J. Wood, Bicategories of spans as cartesian bicategories, TAC 24 (1).