Historically, a great many features of organisms have been said to show a trend over the history of life, and many rationales for such trends have been proposed. Here I review eight candidates, eight 'live hypotheses' that are inspiring research on largest-scale trends today: entropy, energy intensiveness, evolutionary versatility, developmental depth, structural depth, adaptedness, size, and complexity. For each, the review covers the principal arguments that have been advanced for why a trend is expected, as well as some of the empirical approaches that have been adopted. Also discussed are three conceptual matters arising in connection with trend studies: 1. Alternative bases for classifying trends: pattern versus dynamics; 2. alternative modes in which largest-scale trends have been studied: 'exploratory' versus 'skeptical'; and 3. evolutionary progress.