Computational learning theory provides a mathematical framework for rigorously formulating learning problems from both a statistical and computational perspective. During this talk I will present two independent results at the interplay of learning theory and quantum computation. First, I will address the problem: “can we learn faster with a quantum computer?”. In particular, I will discuss the learnability of the class of boolean functions that can be expressed as polynomial size formulae in disjunctive normal form (DNF) and show that this is efficiently quantum PAC learnable under product distributions. The learnability of DNFs is a central problem in learning theory and the best known classical algorithm (using standard ways to access the function) runs in superpolynomial time. Second, I will discuss the problem “what it means to learn a quantum state and can we do that efficiently?”. Here, building on a model developed by Aaronson in 2007, I will present a class of states, namely stabiliser states, that can be learned using only a linear number of measurements and polynomial - classical - computation. Part of the results are joint work with Varun Kanade and Simone Severini.