Learning to generate diverse scene-aware and goal-oriented human motions in 3D scenes remains challenging due to the mediocre characters of the existing datasets on Human-Scene Interaction (HSI); they only have limited scale/quality and lack semantics. To fill in the gap, we propose a large-scale and semantic-rich synthetic HSI dataset, denoted as HUMANISE, by aligning the captured human motion sequences with various 3D indoor scenes. We automatically annotate the aligned motions with language descriptions that depict the action and the individual interacting objects; e.g., sit on the armchair near the desk. HUMANIZE thus enables a new generation task, language-conditioned human motion generation in 3D scenes. The proposed task is challenging as it requires joint modeling of the 3D scene, human motion, and natural language. To tackle this task, we present a novel scene-and-language conditioned generative model that can produce 3D human motions of the desirable action interacting with the specified objects. Our experiments demonstrate that our model generates diverse and semantically consistent human motions in 3D scenes.