Experimental observations of the growth and collapse of acoustically and laser-nucleated single bubbles in water and agarose gels of varying stiffness are presented. The maximum radii of generated bubbles decreased as the stiffness of the media increased for both nucleation modalities, but the maximum radii of laser-nucleated bubbles decreased more rapidly than acoustically nucleated bubbles as the gel stiffness increased. For water and low stiffness gels, the collapse times were well predicted by a Rayleigh cavity, but bubbles collapsed faster than predicted in the higher stiffness gels. The growth and collapse phases occurred symmetrically (in time) about the maximum radius in water but not in gels, where the duration of the growth phase decreased more than the collapse phase as gel stiffness increased. Numerical simulations of the bubble dynamics in viscoelastic media showed varying degrees of success in accurately predicting the observations.