Active fold-and-thrust belts and accretionary wedges along compressive plate boundaries are analogous to the wedges of soil or snow that form in front of moving bulldozers. Such wedges deform until they attain a critical taper, which corresponds to an internal state of stress that is everywhere on the verge of Coulomb failure. The critical taper depends on the wedge cohesion S0 as well as the internal and basal coefficients of friction μ and μb and the internal and basal Hubbert-Rubey pore-fluid pressure ratios λ and λb; an exact relation can be obtained if the cohesion increases linearly with depth, i.e., S0 =Kz. Typical laboratory rock-strength parameters in the range μ = μb = 0.6 to 0.85 and S0 = 5 to 18 MPa are consistent with the known taper, thrust-fault dips, and pore-fluid pressures in the western Taiwan fold-and-thrust belt. Much lower rock strengths in the range μ = μb ≈ 0.2 and S0 ≈ 0, however, can also satisfy the Taiwan data. As fresh material enters the toe of a fold-and-thrust belt, accretionary wedge, or bulldozer wedge, the wedge grows self-similarly, maintaining its critical taper. A submarine or other noneroding wedge widens with time like t1/2, whereas an eroding wedge attains a steady-state width when the accretionary influx is balanced by erosion. The rate of erosion exerts a significant control on the deformation and metamorphic histories of rocks incorporated into mountain belts. To illustrate this, we develop a simple kinematical model of self-similar wedge growth, and use it to infer the mean trajectories and residence times of rocks in the rapidly eroding fold-and-thrust belt in central Taiwan, which develops a steady-state width of about 90 km. A typical rock resides in the Taiwan wedge for 2 to 3 m.y. before being uplifted and eroded, and it experiences strain rates in the range ∊̇ = 10−13 to 10−14 s−1 and finite strains in the range S = 1 to 10. Qualitatively, the model predicts that rocks transported farther into the wedge have been buried deeper and thus have been subjected to greater pressures and temperatures, in general agreement with the observed gradient of metamorphism in Taiwan and other mountain belts. In contrast with rapidly eroding mountain belts like Taiwan, more slowly eroding belts can grow to widths in excess of 300 to 500 km and have mean residence times greater than 50 m.y., which may be too long to reach true steady state before conditions change.