Bubbles in complex fluids are often desirable, and sometimes simply
inevitable, in the processing of formulated products. Bubbles can rise by
buoyancy, grow or dissolve by mass transfer, and readily respond to changes in
pressure, thereby applying a deformation to the surrounding complex fluid. The
deformation field around a stationary, spherical bubble undergoing a change in
radius is simple and localised, thus making it suitable for rheological
measurements. This article reviews emerging approaches to extract information
on the rheology of complex fluids by analysing bubble dynamics. The focus is on
three phenomena: changes in radius by mass transfer, harmonic oscillations
driven by an acoustic wave, and bubble collapse. These phenomena cover a broad
range of deformation frequencies, from $10^{-4}$ to $10^6$ Hz, thus paving the
way to broadband microrheology using bubbles as active probes. The outstanding
challenges that need to be overcome to achieve a robust technique are also
discussed