Prominence seismology is a rapidly developing topic which seeks to infer the internal structure and properties of solar prominences from the study of their oscillations. An extense observational background about oscillations in quiescent solar prominences has been gathered during the last 70 years. These observations point out the existence of two different types of oscillations: flare-induced oscillations (winking filaments) which affect the whole prominence and are of large amplitude and small amplitude oscillations which seem to be of local nature. From the theoretical point of view, few models have been set up to explain the phenomenon of winking filaments while, on the contrary, for small amplitude oscillations a large number of models trying to explain the observed features have been proposed. Here, recent theoretical and observational developments on both types of oscillations are reviewed, and suggestions about future research topics which should provide us with a more in-depth knowledge of solar prominences are made.