String gas cosmology: progress and problems

String gas cosmology is a model of the evolution of the very early universe based on fundamental principles and key new degrees of freedom of string theory which are different from those of point particle field theories. In string gas cosmology the universe starts in a quasi-static Hagedorn phase during which space is filled with a gas of highly excited string states. Thermal fluctuations of this string gas lead to an almost scale-invariant spectrum of curvature fluctuations. Thus, string gas cosmology is an alternative to cosmological inflation as a theory for the origin of structure in the universe. This short review focuses on the building blocks of the model, the predictions for late time cosmology, and the main problems which the model faces.