From the time the first stars formed over 13 billion years ago to the present, star formation has had an unexpectedly dynamic history. At first, the star-formation rate density increased dramatically, reaching a peak 10 billion years ago of more than 10 times the present-day value. Observations of the initial rise in star formation remain difficult, poorly constraining it. Theoretical modeling has trouble predicting this history because of the difficulty in following the feedback of energy from stellar radiation and supernova explosions into the gas from which further stars form. Observations from the ground and space with the next generation of instruments should reveal the full history of star formation in the universe, and simulations appear poised to accurately predict the observed history.