This paper develops new designs for recommendation systems inspired by recent advances in graph signal processing. Recommendation systems aim to predict unknown ratings by exploiting the information revealed in a subset of user-item observed ratings. Leveraging the notions of graph frequency and graph filters, we demonstrate that classical collaborative filtering methods, such as k -nearest neighbors (NN), can be modeled as a specific band-stop graph filter on networks describing similarities between users or items. We also demonstrate that linear latent factor (LF) models, such as low-rank matrix completion, can be viewed as bandlimited interpolation algorithms that operate in a frequency domain given by the spectrum of a joint user and item network. These new interpretations pave the way to new methods for enhanced rating prediction. For NN-based collaborative filtering, we develop more general band-stop graph filters, and present a novel predictor, called mirror filtering (MiFi), that filters jointly across user and item networks. For LF, we propose a low complexity method by exploiting the eigenvector of correlation matrices constructed from known ratings. The performance of our algorithms is assessed in the MovieLens 100 k dataset, showing that our designs reduce the root mean-squared error (up to a 6.85% for MiFi) compared to one incurred by the benchmark collaborative filtering approach.