Human beings, even small children, quickly become adept at figuring out how to use applications on their mobile devices. Learning to use a new app is often achieved via trial-and-error, accelerated by transfer of knowledge from past experiences with like apps. The prospect of building a smarter smartphone — one that can learn how to achieve tasks using mobile apps — is tantalizing. In this paper we explore the use of Reinforcement Learning (RL) with the goal of advancing this aspiration. We introduce an RL-based framework for learning to accomplish tasks in mobile apps. RL agents are provided with states derived from the underlying representation of on-screen elements, and rewards that are based on progress made in the task. Agents can interact with screen elements by tapping or typing. Our experimental results, over a number of mobile apps, show that RL agents can learn to accomplish multi-step tasks, as well as achieve modest generalization across different apps. More generally, we develop a platform which addresses several engineering challenges to enable an effective RL training environment. Our AppBuddy platform is compatible with OpenAI Gym and includes a suite of mobile apps and benchmark tasks that supports a diversity of RL research in the mobile app setting.