Language is central to human intelligence. We review recent break- throughs in machine language processing and consider what re- mains to be achieved. Recent approaches rely on domain general principles of learning and representation captured in artificial neu- ral networks. Most current models, however, focus too closely on language itself. In humans, language is part of a larger system for acquiring, representing, and communicating about objects and sit- uations in the physical and social world, and future machine lan- guage models should emulate such a system. We describe exist- ing machine models linking language to concrete situations, and point toward extensions to address more abstract cases. Human language processing exploits complementary learning systems, in- cluding a deep neural network-like learning system that learns grad- ually as machine systems do, as well as a fast-learning system that supports learning new information quickly. Adding such a system to machine language models will be an important further step toward truly human-like language understanding.