The goal of machine translation (MT) is to translate text from one natural language to another. Linguistic properties of the languages involved, and rich morphology in particular, play an important role in the difficulty of the task. After a brief survey of history of MT and morphologically rich languages (MRLs), the whole ‘MT pipeline’ is introduced, covering all the steps needed in the development of an MT system. The current mainstream approach, is highlighted, that is the phrase-based MT. The chapter the reader through the MT pipeline, explaining in detail how rich morphology negatively affects each of the steps, including the evaluation of MT quality. A wider range of MT system types is covered in the last section where old and contemporary methods for explicit and more linguistically adequate handling of rich morphology are surveyed.