Talk given at Dark Matter 2000, Marina del Rey, CA, February 2000; (astro-ph/0005265)
Abstract. The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.
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* This research was supported in part by the Robert A. Welch Foundation and NSF Grant PHY-9511632.