Many of the representations of Condorcet domains presented so far crucially hinge on the fact that we are considering strict linear orders (i.e. permutations) of the alternatives. However, economically meaningful domain restrictions such a single-peakedness and single-crossingness are naturally generalisable to weak orders and even partial orders. In this chapter, we present some basic facts and results about Condorcet domains of weak and partial orders. We do not aim at a comprehensive treatment but rather highlight the main differences and similarities to the case of linear orders in the hope to stimulate further research along this, so far unexplored route.