  Gauge symmetries are a cornerstone of modern physics but they come with
technical difficulties when it comes to quantization, to accurately describe
particles phenomenology or to extract observables in general. These
shortcomings must be met by essentially finding a way to effectively reduce
gauge symmetries. We propose a review of a way to do so which we call the
dressing field method. We show how the BRST algebra satisfied by gauge fields,
encoding their gauge transformations, is modified. We outline noticeable
applications of the method, such as the electroweak sector of the Standard
Model and the local twistors of Penrose.
