Computational autopoiesis--the realization of autopoietic entities in computational media--holds an important and distinctive role within the field of artificial life. Its earliest formulation by Francisco Varela, Humberto Maturana, and Ricardo Uribe was seminal in demonstrating the use of an artificial, computational medium to explore the most basic question of the abstract nature of living systems--over a decade in advance of the first Santa Fe Workshop on Artificial Life. The research program it originated has generated substantive demonstrations of progressively richer, lifelike phenomena. It has also sharply illuminated both conceptual and methodological problems in the field. This article provides an integrative overview of the sometimes disparate work in this area, and argues that computational autopoiesis continues to provide an effective framework for addressing key open problems in artificial life.