The Hammond organ is an early electronic musical instrument, which was popular in the 1960s and 1970s. This paper proposes computationally efficient models for the Hammond organ and its rotating speaker system, the Leslie. Organ tones are generated using additive synthesis with appropriate features, such as a typical fast attack and decay envelope for the weighted sum of the harmonics and a small amplitude modulation simulating the construction inaccuracies of tone wheels. The key click is realized by adding the sixth harmonic modulated by an additional envelope to the original organ tone. For the Leslie speaker modeling we propose a new approach, which is based on time-varying spectral delay filters producing the Doppler effect. The resulting virtual organ, which is conceptually easy, has a pleasing sound and is computationally efficient to implement.