Let $G$ be a finite group and $k$ a field of characteristic $p>0$. In this talk, we will introduce the notion of an endotrivial chain complex, a generalization of an endotrivial $kG$-module. Such chain complexes induce examples of splendid Rickard autoequivalences. We introduce multiple "relative" versions of these chain complexes as well, which rely on projectivity relative to a $kG$-module $V$. In fact, (relatively) endotrivial chain complexes can be determined almost entirely, up to homotopy and projectives, by local homological data. As a result, we obtain structural results partially describing the groups which parametrize (relative) endotrivial complexes. In this talk, we will build up to describing these results, and, if time permits, describe how a particular class of relatively endotrivial complexes, as well as the theory of endopermutation modules, can be used to completely describe all of the endotrivial complexes for a $p$-group.