How do firms respond to technological advances that facilitate the automation of tasks? Which tasks will they automate, and what types of worker will be replaced as a result? We present a model that distinguishes between a task's engineering complexity and its training requirements. When two tasks are equally complex, firms will automate the task that requires more training and in which labor is hence more expensive. Under quite general conditions this leads to job polarization, a decline in middle wage jobs relative to both high and low wage jobs. Our theory explains recent and historical instances of job polarization as caused by labor-replacing technologies, such as computers, the electric motor, and the steam engine, respectively. The model makes novel predictions regarding occupational training requirements, which we find to be consistent with US data.