  This chapter introduces the main ideas and the most important methods for
representing the electronic wavefunction through machine learning models. The
wavefunction of a N-electron system is an incredibly complicated mathematical
object, and models thereof require enough flexibility to properly describe the
complex interactions between the particles, but at the same time a sufficiently
compact representation to be useful in practice. Machine learning techniques
offer an ideal mathematical framework to satisfy these requirements, and
provide algorithms for their optimization in both supervised and unsupervised
fashions. In this chapter, various examples of machine learning wavefunctions
are presented and their strengths and weaknesses with respect to traditional
quantum chemical approaches are discussed; first in theory, and then in
practice with two case studies.
