Recent studies have shown that when bilinguals or multilinguals read written words, listen to spoken words, or plan words that they intend to speak in one language alone, information in all of the languages that they know is momentarily active. That activation produces cross-language competition that sometimes converges to facilitate performance and sometimes diverges to create costs to performance. The presence of parallel activation across languages has been documented in comprehension, in studies of word recognition, and also in production, in studies of lexical speech planning. The observation that one of the two or more languages cannot be switched off at will is particularly surprising in production, where the intention to express a thought should be guided by conceptually driven processes. Likewise, in comprehension, recent studies show that placing words in sentence context in one language alone is insufficient to restrict processing to that language. The focus of current research on the multilingual lexicon is therefore to understand the basis of language nonselectivity, to consider how the language in use is ultimately selected, and to identify the cognitive consequences of having a lexical system that is open to influence by the languages not in use. In this article, we review the recent cognitive and neural evidence on each of these issues, with special consideration to the question of how the nature of the evidence itself shapes the conclusions drawn about the organization and access to the lexicon in individuals who speak more than one language.