Runup of debris flows against obstacles in their paths is a complex process that involves profound flow deceleration and redirection. We investigate the dynamics and predictability of runup by comparing results from large-scale laboratory experiments, four simple analytical models, and a depth-integrated numerical model (D-Claw). The experiments and numerical simulations reveal the important influence of unsteady, multidimensional flow on runup, and the analytical models highlight key aspects of the underlying physics. Runup against a vertical barrier normal to the flow path is dominated by rapid development of a shock, or jump in flow height, associated with abrupt deceleration of the flow front. By contrast, runup on sloping obstacles is initially dominated by a smooth flux of mass and momentum from the flow body to the flow front, which precedes shock development and commonly increases the runup height. D-Claw simulations that account for the emergence of shocks show that predicted runup heights vary systematically with the adverse slope angle and also with the Froude number and degree of liquefaction (or effective basal friction) of incoming flows. They additionally clarify the strengths and limitations of simplified analytical models. Numerical simulations based on a priori knowledge of the evolving dynamics of incoming flows yield quite accurate runup predictions. Less predictive accuracy is attained in ab initio simulations that compute runup based solely on knowledge of static debris properties in a distant debris flow source area. Nevertheless, the paucity of inputs required in ab initio simulations enhances their prospective value in runup forecasting.