Unmanned Aerial Systems (UAS) are being increasingly deployed for commercial, civilian, and military applications. The current UAS state-of-the-art still depends on a remote human controller with robust wireless links to perform several of these applications. The lack of autonomy restricts the domains of application and tasks for which a UAS can be deployed. Enabling autonomy and intelligence to the UAS will help overcome this hurdle and expand its use improving safety and efficiency. The exponential increase in computing resources and the availability of large amount of data in this digital era has led to the resurgence of machine learning from its last winter. Therefore, in this chapter, we discuss how some of the advances in machine learning, specifically deep learning and reinforcement learning can be leveraged to develop next-generation autonomous UAS. We first begin motivating this chapter by discussing the application, challenges, and opportunities of the current UAS in the introductory section. We then provide an overview of some of the key deep learning and reinforcement learning techniques discussed throughout this chapter. A key area of focus that will be essential to enable autonomy to UAS is computer vision. Accordingly, we discuss how deep learning approaches have been used to accomplish some of the basic tasks that contribute to providing UAS autonomy. Then we discuss how reinforcement learning is explored for using this information to provide autonomous control and navigation for UAS. Next, we provide the reader with directions to choose appropriate simulation suites and hardware platforms that will help to rapidly prototype novel machine learning based solutions for UAS. We additionally discuss the open problems and challenges pertaining to each aspect of developing autonomous UAS solutions to shine light on potential research areas.