We investigate the global structure of an inflationary universe both by analytical methods and by computer simulations of stochastic processes in the early Universe. We show that the global structure of an inflationary universe depends crucially on the mechanism of inflation. In the simplest models of chaotic inflation with the effective potentials ${\mathrm{\phi }}^{\mathit{n}}$ or ${\mathit{e}}^{\mathrm{\alpha }\mathrm{\phi }}$ the Universe looks like a sea of a thermalized phase, surrounding permanently self-reproducing inflationary domains. On the other hand, in the theories where inflation may occur near a local extremum of the effective potential corresponding to a metastable state, the Universe looks like de Sitter space surrounding islands of a thermalized phase. A similar picture appears even if the state φ=0 is unstable but the effective potential has a discrete symmetry, e.g., the symmetry φ→=-φ. In this case the Universe becomes divided into domains containing different phases (η or -η). These domains will be separated from each other by domain walls. However, unlike ordinary domain walls often discussed in the literature, these domain walls will inflate, and their thickness will exponentially grow. In the theories with continuous symmetries, inflation will generate exponentially expanding strings and monopoles surrounded by a thermalized phase. Inflating topological defects will be stable, and they will unceasingly produce new topological defects. This means that topological defects may play a role of indestructable seeds for eternal inflation.

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