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Electron cyclotron heating by high-power microwave beams is a key method for plasma heating in tokamaks and stellarators. Under some conditions, these beams engage in nonlinear three-wave interactions, known as parametric decay instabilities (PDIs), where energy is transferred from the main beam to two downshifted waves. PDIs are well documented to occur during fundamental electron Bernstein wave heating, with observations in multiple devices. However, PDIs were overlooked in the more common second-harmonic electron cyclotron heating until recently, when nonlinear scattering was observed. This has been attributed to a class of absolute PDIs that involves wave trapping in density fluctuations. Here we provide an overview of recent numerical and experimental results in the study of PDIs. We show direct observations of PDIs at the devices ASDEX Upgrade, TCV, Wendelstein 7-X, and NORTH, and show that the occurrence of PDIs is correlated with density fluctuations in the scrape-off layer caused by ELMs and blobs as well as density fluctuations in the plasma core due to NTMs. We outline the consequences of PDI occurrence, which could include a decrease in heating efficiency and an associated fast-ion production. In addition, we discuss possible schemes for exploiting PDIs, including controlled energy transfer to selected plasma waves and potential diagnostic techniques for density fluctuations.