Humans are extremely efficient in learning concepts and in forming new concepts. However, some conceptual systems are more efficient than others. One of the central tasks for conceptual engineering is to construct systems that fulfil some criteria of optimality. I argue that the methods of Knowledge Representation and Machine Learning are not sufficient. This chapter instead proposes that conceptual engineers should use conceptual spaces, which are based on using geometric structures rather than symbols or connections between neurons. Essential aspects of concept learning and concept changes are best described in such spatial structures. The chapter consists of three parts. The first is devoted to describing criteria for natural concepts and how to model them in conceptual spaces. The role of these criteria for the philosophical debate on conceptual engineering is briefly discussed. The second part deals with the composition of concepts into sentential structures, where a cognitive model of events provides the fundamental semantic structure. The third part briefly discusses issues related to implementations.