This article presents an overview of recent methodological advances in developing nearest-neighbor-based recommender systems that have substantially improved their performance. The key components in these methods are: (i) the use of statistical learning to estimate from the data the desired user-user and item-item similarity matrices, (ii) the use of lower-dimensional representations to handle issues associated with data sparsity, (iii) the combination of neighborhood and latent space models, and (iv) the direct incorporation of auxiliary information during model estimation. The article will also provide illustrative examples for these methods in the context of item-item nearest-neighbor methods for rating prediction and Top-N recommendation. In addition, the article will present an overview of exciting new application areas of recommender systems along with the challenges and opportunities associated with them.