Real-world applications of deep learning often have to contend with objectives beyond predictive performance, i.e., more than one equally important and competing objective or criterion. Examples include cost functions pertaining to invariance (e.g., to photometric or geometric variations), semantic independence (e.g., to age or race for face recognition systems), privacy (e.g., mitigating leakage of sensitive information), algorithmic fairness (e.g., demographic parity), generalization across multiple domains, computational complexity (FLOPs, compactness), to name a few. In such applications, achieving a single solution that simultaneously optimizes all objectives is no longer feasible; instead, finding a set of solutions that are representative in describing the trade-off among objectives becomes the goal. Multiple approaches have been developed for such problems, including simple scalarization and population-based methods. This tutorial aims to provide a comprehensive introduction to fundamentals, recent advances, and applications of multi-objective optimization (MOO), followed by hands-on coding examples. Some emerging applications of MOO include (1) hardware-aware neural architecture search; (2) multi-task learning as multi-objective optimization; (3) representation learning for privacy and fairness. We will also summarize potential research directions intersecting MOO and ML/CV research.