We have compiled historical observations, spanning ∼100 years, for a dozen of the best-studied LBVs in the Local Group. We described how we prepared structure functions for their light-curves and calculated two parameters (the structure function slope and the characteristic time-scale) to describe the behaviour of the LBVs. The sensitivity of those parameters to the variability behaviour of the stars was tested with a number of photometric data sets. The slope of the structure function may anticorrelate with the time-scale. These types of variable stellar objects are crucial to studies of stellar variability and the final stages of stellar evolution.

Wolf-Rayet (WR) stars and their possible precursors, the Luminous Blue Variables (LBVs), are often surrounded by ring nebulae. It is believed that these nebulae are formed by the action of the stellar wind, matter being ejected from the star in the past, or a combination of these two processes. The various research applications of LBV and WR nebulae are reviewed with regard to the information they provide on the properties of the central stars. They are very useful probes of stellar evolution since the details of the previous evolutionary phases of the central stars are contained in the nebulae. In particular, abundance studies can provide insights into the chemical processes operating during the precursor phases. The nebulae can also be used as probes of the far-UV ionizing flux distribution of the central WR stars by comparing the observed levels of nebular ionization with those produced with non-LTE WR model flux distributions. Comparisons of stellar effective temperatures and luminosities derived using this technique with those determined by modelling stellar emission lines can identify deficiencies such as the lack of line-blanketing in WR model atmospheres. Very hot WR stars can also be identified by searching for nebular HeII emission. Studies of bipolar structures in LBV and WR nebulae provide valuable clues on wind asymmetries in the central stars.