This talk will present the modeling of multiple protein sequence alignment (MSA) by Markov Random Fields (MRF) and its applications to homology detection, evolutionary coupling analysis and protein folding. In particular, this talk will cover 1) modeling a set of related protein families (each represented as an MSA) by group graphical lasso and its application to joint evolutionary coupling analysis and protein contact prediction; and 2) aligning two MSAs by aligning their respective MRFs and its application to homology detection and fold recognition.