Fish swimbladders can serve as sound-producing organs and accessory auditory organs that transfer vibrations to the ears. Since the 1960s swimbladders have been modelled acoustically as underwater bubbles, resonant monopoles that radiate sound omni-directionally. Data inconsistent with this paradigm are typically dismissed as the result of damping by surrounding fish tissues. Fish sonic swimbladder muscles are among the fastest in vertebrates, which should be unnecessary to excite a resonant structure. Recent work however indicates that toadfish, weakfish and black drum produce sounds as a forced response whose frequency is determined by muscle contraction and not the resonant frequency of the bladder. Furthermore, the natural frequency of toadfish sounds does not vary inversely with fish size, and damping is equivalent to that of an automobile shock absorber, a device designed to suppress resonance. Toadfish produce a directional (not omnidirectional) sound field consistent with swimbladder shape, and deflation of the bladder does not change auditory thresholds. To our surprise, we recently discovered that carapid fish utilize slow muscles to produce sounds. Their swimbladder has an elastic fenestra covered by a bony plate that we believe drives the swimbladder following muscle contraction. We suggest that related ophidiid fishes, one of the commonest groups in the deep-sea bottom also have slow muscles because some species have a fenestra and muscles that occur in antagonistic pairs. Paradoxically, the striped cusk-eel produces the highest peak frequency known for swimbladder sounds, likely with a slow muscle. Fish swimbladder walls are anisotropic structures with a high water content composed of collagen. They are likely responsible for rapid damping of swimbladder sounds, and we suggest that sounds produced by slow muscles utilize additional mechanisms to drive high frequency vibrations from a structure that would otherwise damp rapidly.