In this talk, I will highlight some recent progress in my group on two related research topics: multi-object rearrangement and discrete multi-body motion planning. Object rearrangement represents an everyday task being constantly carried out everywhere, e.g., tidying a desk, sorting out-of-order groceries on shelves, picking and packing food items from a conveyor belt, to list a few. As it turns out, interesting TSP and feedback vertex set problems naturally come out of typical multi-object rearrangement tasks, which can be solved accordingly. On the side of multi-body motion planning, I will outline some recent effort in characterizing the achievable optimality in well-connected environment, with associated algorithms that achieve the corresponding optimality guarantees.