Single-mode (SM) fiber lasers and amplifiers are constrained to low output powers by fundamental physical limitations of the fiber, specifically, by low energy storage and by the onset of nonlinear processes in the fiber. The simplest way to overcome both limiting factors is to increase the core size, but maintaining SM operation imposes an upper limit. Further power scaling is possible with multimode (MM) fiber, but the poor beam quality generally associated MM fiber is unacceptable for many applications. We have developed a technique (bend-loss-induced mode filtering) that allows the core size to be increased significantly beyond the SM limit while maintaining diffraction-limited beam quality and high efficiency. In this method, coiling of the fiber is used as a form of distributed spatial filtering to suppress all but the fundamental mode of a highly MM fiber amplifier. Unlike conventional spatial filtering, in which high-order modes are discarded, the mode-filtering technique does not result is substantial loss of efficiency because high-order modes are suppressed along the entire length of the amplifier and are thus prevented from building up significant intensity. We will review this method and recent experimental results for both cw and pulsed fiber sources, including nonlinear frequency conversion of mode-filtered fiber lasers. Optical damage issues will also be discussed.