We present and study the current research trends and advances for optimizing assemble-to-order systems with stochastic lead times. Assemble-to-order systems are widely used in several industries, where end products consist of multiple components and are customizable. Manufacturers can offer greater flexibility to their customers by delaying the assembly of the components until after the order is placed. This means they do not keep an inventory of end-products. Only components can be kept in the inventory and assembled upon demand. We compare and contrast different formulations and the features of assemble-to-order systems studied in the literature including system configuration, replenishment policy, lead time type, and demand distribution. Single-period systems, periodic-review systems, and continuous-review systems are considered. Current assumptions, formulations, solutions, and challenges are discussed. / Thesis / Master of Science (MSc)