Cosmology presents intriguing issues for the understanding and tracking of time. The big bang theory says that the universe began 13.8 billion years ago, in a situation of almost unimaginable temperature and density. The age of the universe is highly constrained by the world model, as long as there are reliable measurements of the current expansion rate (the Hubble constant), and amounts of baryonic matter, dark matter, and dark energy. A crucial cross-check on the model age comes from stellar chronometers and the ages of the oldest stars in the Milky Way. Landmarks in cosmic evolution reach back to about 380,000, years (recombination), 40,000, years (matter domination), and a few minutes (light element creation) after the big bang. Time in Newtonian cosmology is absolute, linear, and eternal, whereas time in the modern cosmology is governed by Einstein’s general relativity, a geometric theory which embodies a profound connection between space and time. In relativity, objects travel on paths called world lines in four-dimensional spacetime. Relativity defines proper time as time measured by an observer with a clock following a world line. A clock in motion relative to the observer, or in a different gravity situation, will not measure proper time. The time concept rests on the cosmological principle—the assumption that the universe is homogeneous and isotropic on large scales. If that is true, there are well-defined relationships between time, scale factor, and temperature going all the way back to the first fraction of a second after the big bang. Time in the far future of the universe can be measured in terms of physical processes—the spinning down of pulsars and the evaporation of black holes. There are still profound physical and philosophical issues raised by the definition of clocks and observers in cosmology.