We present 3D Pick & Mix, a new 3D shape retrieval system that provides users with a new level of freedom to explore 3D shape and Internet image collections by introducing the ability to reason about objects at the level of their constituent parts. While classic retrieval systems can only formulate simple searches such as "find the 3D model that is most similar to the input image" our new approach can formulate advanced and semantically meaningful search queries such as: "find me the 3D model that best combines the design of the legs of the chair in image 1 but with no armrests, like the chair in image 2". Many applications could benefit from such rich queries, users could browse through catalogues of furniture and pick and mix parts, combining for example the legs of a chair from one shop and the armrests from another shop.