In recent years, reinforcement learning and bandits have transformed a wide range of real-world applications including healthcare, finance, recommendation systems, robotics, and last but not least, the speech and natural language processing. While most speech and language applications of reinforcement learning algorithms are centered around improving the training of deep neural networks with its flexible optimization properties, there are still many grounds to explore to utilize the benefits of reinforcement learning, such as its reward-driven adaptability, state representations, temporal structures and generalizability. In this survey, we present an overview of recent advancements of reinforcement learning and bandits, and discuss how they can be effectively employed to solve speech and natural language processing problems with models that are adaptive, interactive and scalable.