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The nonuniform trial length problem, which causes information dropout in learning, is very common in various control systems such as robotics and motion control systems. This paper presents a comprehensive survey of recent progress on iterative learning control with randomly varying trial lengths. Related works are reviewed in three dimensions: model, synthesis, and convergence analysis. Specifically, we first present both random and deterministic models of varying trial lengths to provide a mathematical description and to reveal the effects and difficulties of nonuniform trial lengths. Then, control synthesis focusing on compensation mechanisms for the missing information and key ideas in designing control algorithms are summarized. Lastly, four representative convergence analysis approaches are elaborated, including deterministic analysis approach, switching system approach, contraction mapping …