Mobile devices (e.g., smartphones) play a crucial role in our daily lives nowadays. People rely heavily on mobile devices for searching online, sending emails, chatting with friends, etc. As a result, input efficiency becomes increasingly important for real-time communication on mobile devices. Due to the small size of the screen on mobile devices, however, it is oftentimes frustrating for users to correct or update the input sequences on an even smaller input area on the screen. This often causes poor user experience. In this paper, we focus on improving the input efficiency on mobile devices to offer better user experience. In order to achieve efficient input, there are multiple challenges: 1) how to employ a single, unified representation of the keyboard layouts for different input languages; 2) how to build a framework to correct a mistouch immediately and predict the coming input texts (words or phrases) effectively; 3) how to deploy and evaluate the model on mobile devices with limited computational power. To address these challenges, we introduce FastInput to improve the user input efficiency on mobile devices. Three key techniques are developed in FastInput - layout modeling, instant mistouch correction and user input text prediction. We also design solutions for efficient deployment and evaluation of FastInput on mobile devices. The proposed FastInput achieves higher efficiency compared to the traditional input system over millions of user input sequences in different languages.