Explore a 14-minute conference talk that delves into the intriguing world of quantum phase operators. Uncover the historical context and Dirac's dilemma before diving into the definition of phase operators in quantum harmonic oscillators. Examine Dirac's initial attempt and its challenges, followed by Lewis's alternative approach. Discover Susskind and Glogover's novel approach, as well as Pegg and Barnett's finite dimensional subspace method. Learn how to build a valid phase operator and gain insights into recent advancements and applications in the field. Conclude with a discussion on future directions, providing a comprehensive overview of this elusive quantum concept.