I will review an experimentally feasible procedure for converting a quantum state into a succinct classical description of the state, its classical shadow. Classical shadows can be applied to predict efficiently many properties of interest, including expectation values of local observables and few-body correlation functions. Efficient classical machine learning algorithms using classical shadows can address quantum many-body problems such as classifying quantum phases of matter. I will also explain how experiments that exploit quantum memory can learn properties of a quantum system far more efficiently than conventional experiments.