  Both simplicial sets and simplicial spaces are used pervasively in homotopy
theory as presentations of spaces, where in both cases we extract the
"underlying space" by taking geometric realization. We have a good handle on
the category of simplicial sets in this capacity; this is due to the existence
of a suitable model structure thereon, which is particularly convenient to work
with since it enjoys the technical properties of being *proper* and of being
*cofibrantly generated*. This paper is devoted to showing that, if one is
willing to work $\infty$-categorically, then one can manipulate simplicial
spaces exactly as one manipulates simplicial sets. Precisely, this takes the
form of a proper, cofibrantly generated model structure on the
*$\infty$-category* of simplicial spaces, the definition of which we also
introduce here.
