We study regular Schwarzschild black holes in general relativity as an alternative to the singular counterpart. We analyze two types of solutions which are completely parametrized by the Arnowitt-Deser- Misner mass alone. We find that both families of regular solutions contain a de Sitter condensate at the core and admit (quasi) extremal black hole configurations in which the two horizons are arbitrarily close. Cosmological models based on these regular configurations are also analyzed, finding that they describe nontrivial Kantowski-Sachs universes free of singularities.