Nutrient-based meal recommendations have the potential to help individuals prevent or manage conditions such as diabetes and obesity. However, learning people's food preferences and making recommendations that simultaneously appeal to their palate and satisfy nutritional expectations are challenging. Existing approaches either only learn high-level preferences or require a prolonged learning period. We propose Yum-me, a personalized nutrient-based meal recommender system designed to meet individuals' nutritional expectations, dietary restrictions, and fine-grained food preferences. Yum-me enables a simple and accurate food preference profiling procedure via a visual quiz-based user interface, and projects the learned profile into the domain of nutritionally appropriate food options to find ones that will appeal to the user. We present the design and implementation of Yum-me, and further describe and evaluate two innovative components: 1) An open source state-of-the-art food image analysis model, named FoodDist. We demonstrate FoodDist's superior performance through careful benchmarking, and discuss its applicability across a wide array of dietary applications. 2) A novel online learning framework that learns food preference from itemwise and pairwise image comparisons. We evaluate the framework in a field study of 227 anonymous users and demonstrate that it outperforms other baselines by a significant margin. Finally, we conduct an end-to-end validation of the feasibility and effectiveness of Yum-me through a 60-person user study, in which Yum-me improves the recommendation acceptance rate by 42.63%.