Robots are becoming more and more capable at reasoning about people, objects, and activities in their environments. The ability to extract high-level semantic information from sensor data provides new opportunities for human robot interaction. One such opportunity is to explore interacting with robots via natural language. In this talk I will present our recent work toward enabling robots to interpret, or ground, natural language commands in robot control systems. We build on techniques developed by the semantic natural language processing community on learning combinatory categorial grammars (CCGs) that parse natural language input to logic-based semantic meaning. I will demonstrate results in two application domains: First, learning to follow natural language directions through indoor environments; and, second, learning to ground object attributes via weakly supervised training.