Alloy design is critical to achieving the target performance of industrial components and products. In designing new alloys, there are multiple property requirements, including mechanical, environmental, and physical properties, as well as manufacturability and processability. Computational models and tools to predict properties from alloy compositions and to optimize compositions for multiple objectives are essential in enabling efficient, robust alloy design. Data-driven property models by machine learning (ML) are particularly useful in predicting physical properties with relatively simple dependence on composition, and in predicting complex properties that are too difficult for a physics-based model to achieve with desirable accuracy. In this article, we describe examples of ML applications to model coefficient of thermal expansion, creep and fatigue resistance in designing Ni-based superalloys, and optimization methodologies. We also discuss physics-based microstructure models that have been developed for optimizing heat-treatment conditions to achieve desired microstructures.