Gamification of language learning is a clear trend of recent years. Widespread use of smartphones and the rise of mobile gaming as a popular leisure activity contribute to the popularity of gamification, as application developers can rely on an unprecedented reach of their products and expect acceptance of game-like elements by the users. In terms of content, however, most mobile apps implement traditional language learning activities, such as reading, listening, translating, and solving quizzes. This article discusses gamification of learning natural language grammar with a mobile app WordBricks, based on a concept of more user-centric lab-style experimental activities. WordBricks challenges users to create syntactically accurate sentences by arranging jigsaw-like colored blocks. Users receive instantaneous feedback on the syntactic compatibility each time any two blocks are placed together. This Scratch-inspired virtual language lab harnesses grammar models used in computational linguistics and allows users to discover underlying grammatical constructions through experimentation. The system was evaluated in a number of diverse settings and shows how the principles of gamification can be applied to second-language acquisition. We discuss general features that enable the users to engage in game-playing behavior and analyze open challenges, relevant for a variety of language learning systems.