The inflationary Universe scenario is reviewed. The development of this cosmological scenario began with investigations of (primarily) first order phase transitions. In the context of grand unified theories, the dilemma of an overproduction of magnetic monopoles was resolved by a rapid expansion of the Universe. The original solution to the magnetic monopole problem quickly led to solutions to a host of other cosmological problems such as the horizon-isotropy and flatness-entropy problems. In this review I will take a detailed look at old and new inflation and its many variants including primordial, supersymmetric, chaotic, axionic, R2, stochastic, eternal, superstring, power-law, multiple inflation and other s. Special emphasis will also be given to consequences of inflation such as the generation of energy density perturbations and scalar field fluctuations. Implications for the cosmological baryon asymmetry, cosmic strings and dark matter will also be discussed.