Users' locations are important for many applications such as personalized search and localized content delivery. In this paper, we study the problem of profiling Twitter users' locations with their following network and tweets. We propose a multiple location profiling model (MLP), which has three key features: 1) it formally models how likely a user follows another user given their locations and how likely a user tweets a venue given his location, 2) it fundamentally captures that a user has multiple locations and his following relationships and tweeted venues can be related to any of his locations, and some of them are even noisy, and 3) it novelly utilizes the home locations of some users as partial supervision. As a result, MLP not only discovers users' locations accurately and completely, but also "explains" each following relationship by revealing users' true locations in the relationship. Experiments on a large-scale data set demonstrate those advantages. Particularly, 1) for predicting users' home locations, MLP successfully places 62% users and outperforms two state-of-the-art methods by 10% in accuracy, 2) for discovering users' multiple locations, MLP improves the baseline methods by 14% in recall, and 3) for explaining following relationships, MLP achieves 57% accuracy.