This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on ”Broadband Dielectric Spectroscopy and its Advanced Technological Applications”, held in Perpignan, France, in September 2011. The purpose of the invited presentation at the workshop was to review and summarize the basic theory of fractional dynamics [7, 24, 8, 11, 10, 9, 12, 14, 15, 21, 19, 22, 23] and demonstrate its relevance and application to broadband dielectric spectroscopy [17, 16, 20, 25]. It was argued, that broadband dielectric spectroscopy might be useful to test effective field theories based on fractional dynamics.