In this paper, we review the recent advances in meta-learning theory and show how they can be used in practice both to better understand the behavior of popular meta-learning algorithms and to improve their generalization capacity. This latter is achieved by integrating the theoretical assumptions ensuring efficient meta-learning in the form of regularization terms into several popular meta-learning algorithms for which we provide a large study of their behavior on classic few-shot classification benchmarks. To the best of our knowledge, this is the first contribution that puts the most recent learning bounds of meta-learning theory into practice for the popular task of few-shot classification.