Acoustic cavitation has been found to belong to the class of deterministically chaotic systems [W. Lauterborn and E. Cramer, Phys. Rev. Lett. 47, 1445 (1981); W. Lauterborn and E. Suchla, Phys. Rev. Lett. 53, 2304 (1984)]. Experiments are described in further support of this view by constructing phase spaces from measured data and by determining the fractal dimension of the strange attractors found. As a model of acoustic chaos, a driven spherical cavitation bubble is suggested. This model has been investigated earlier in a simple version [W. Lauterborn, J. Acoust. Soc. Am. 59, 283–293 (1976)]. New results will be given on period-doubling cascades to chaos and on the bifurcation superstructure resulting from the nonlinear resonances.