The idea of this chapter is to show ways to construct polytopes from other polytopes, with emphasis on constructions yielding chiral polytopes. Some of these constructions can be performed through the connection group, and include the well-understood dual and Petrial operations. Other constructions use geometric or topological ideas, like embeddings, quotients and covers. The last construction, called the mix, uses two polytopes to obtain a third polytope that covers the other two.