Although latent factor models (e.g., matrix factorization) achieve good accuracy in rating prediction, they suffer from several problems including cold-start, non-transparency, and suboptimal recommendation for local users or items. In this paper, we employ textual review information with ratings to tackle these limitations. Firstly, we apply a proposed aspect-aware topic model (ATM) on the review text to model user preferences and item features from different aspects, and estimate the aspect importance of a user towards an item. The aspect importance is then integrated into a novel aspect-aware latent factor model (ALFM), which learns user's and item's latent factors based on ratings. In particular, ALFM introduces a weighted matrix to associate those latent factors with the same set of aspects discovered by ATM, such that the latent factors could be used to estimate aspect ratings. Finally, the overall rating is computed via a linear combination of the aspect ratings, which are weighted by the corresponding aspect importance. To this end, our model could alleviate the data sparsity problem and gain good interpretability for recommendation. Besides, an aspect rating is weighted by an aspect importance, which is dependent on the targeted user's preferences and targeted item's features. Therefore, it is expected that the proposed method can model a user's preferences on an item more accurately for each user-item pair locally. Comprehensive experimental studies have been conducted on 19 datasets from Amazon and Yelp 2017 Challenge dataset. Results show that our method achieves significant improvement compared with strong baseline methods, especially for users with only few ratings. Moreover, our model could interpret the recommendation results in depth.