Cucurbituril-type hosts are highly symmetric, but there are means to break their symmetry. This review will present examples from three directions of induction of chirality in or by cucurbituril-type hosts: first, through the incorporation of stereogenic elements into host molecules; second, through complexation with achiral guests, which leads to axial supramolecular chirality and helical structures; third, through the formation of complexes with chiral guests in multi-molecule complexes and induction of supramolecular chirality. In addition, a list of chiral guests used in binding studies with cucurbiturils is collected. We would envision that encouraged by the outlined examples of outstanding applications of chiral cucurbituril-supramolecular systems, the boundaries of chiral applications of cucurbiturils would be widened.