A problem of considerable interest in the hyperspectral and chemical imaging communities in recent years has been the automated identification and mapping of the constituent materials ("endmembers") present in a hyperspectral image. Several of the more important endmember-finding algorithms are discussed and some of their shortcomings highlighted. A relatively new algorithm, ICE, which attempts to address these shortcomings, is introduced. Although ICE was originally developed for exploration applications of airborne hyperspectral data, its performance on two biomedical data sets is investigated. Possible future research directions are outlined.