Although personalized recommendation has been investigated for decades, the wide adoption of Latent Factor Models (LFM) has made the explainability of recommendations a critical issue to both the research community and practical application of recommender systems. For example, in many practical systems the algorithm just provides a personalized item recommendation list to the users, without persuasive personalized explanation about why such an item is recommended while another is not. Unexplainable recommendations introduce negative effects to the trustworthiness of recommender systems, and thus affect the effectiveness of recommendation engines. In this work, we investigate explainable recommendation in aspects of data explainability, model explainability, and result explainability, and the main contributions are as follows: 1. Data Explainability: We propose Localized Matrix Factorization (LMF) framework based Bordered Block Diagonal Form (BBDF) matrices, and further applied this technique for parallelized matrix factorization. 2. Model Explainability: We propose Explicit Factor Models (EFM) based on phrase-level sentiment analysis, as well as dynamic user preference modeling based on time series analysis. In this work, we extract product features and user opinions towards different features from large-scale user textual reviews based on phrase-level sentiment analysis techniques, and introduce the EFM approach for explainable model learning and recommendation. 3. Economic Explainability: We propose the Total Surplus Maximization (TSM) framework for personalized recommendation, as well as the model specification in different types of online applications. Based on basic economic concepts, we provide the definitions of utility, cost, and surplus in the application scenario of Web services, and propose the general framework of web total surplus calculation and maximization. Explainable Recommendation: Theory and Applications