The range, variety, or diversity of words found in learners' language use is believed to reflect the complexity of their vocabulary knowledge as well as the level of their language proficiency. Many indices of lexical diversity have been proposed, most of which involve statistical relationships between types and tokens, and which ultimately reflect the rate of word repetition. These indices have generally been validated in accordance with how well they overcome sample-size effects and/or how well they predict language knowledge or behavior, rather than in accordance with how well they actually measure the construct of lexical diversity. In this article, I review developments that have taken place in lexical diversity research, and also describe obstacles that have prevented it from advancing further. I compare these developments with parallel research on biodiversity in the field of ecology, and show what language researchers can learn from ecology regarding the modeling and measurement of diversity as a multidimensional construct of compositional complexity.