  In this paper we study $d$-dependent random graphs -- introduced by Brody and
Sanchez -- which are the family of random graph distributions where each edge
is present with probability $p$, and each edge is independent of all but at
most $d$ other edges. For this random graph model, we analyze degree sequences,
jumbledness, connectivity, and subgraph containment. Our results mirror those
of the classical Erd\H{o}s--R\'enyi random graph, which are recovered by
specializing our problem to $d=0$, although we show that in many regards our
setting is appreciably more nuanced. We survey what is known for this model and
conclude with a variety of open questions.
