In the last two decades, plasmon resonance in gold nanoparticles (Au NPs) has been the subject of intense research efforts. Plasmon physics is intriguing and its precise modelling proved to be challenging. In fact, plasmons are highly responsive to a multitude of factors, either intrinsic to the Au NPs or from the environment, and recently the need emerged for the correction of standard electromagnetic approaches with quantum effects. Applications related to plasmon absorption and scattering in Au NPs are impressively numerous, ranging from sensing to photothermal effects to cell imaging. Also, plasmon-enhanced phenomena are highly interesting for multiple purposes, including, for instance, Raman spectroscopy of nearby analytes, catalysis, or sunlight energy conversion. In addition, plasmon excitation is involved in a series of advanced physical processes such as non-linear optics, optical trapping, magneto-plasmonics, and optical activity. Here, we provide the general overview of the field and the background for appropriate modelling of the physical phenomena. Then, we report on the current state of the art and most recent applications of plasmon resonance in Au NPs.