Luminescence decay functions describe the time dependence of the intensity of radiation emitted by electronically excited species. Decay phasor plots (plots of the Fourier sine transform vs. the Fourier cosine transform, for one or several angular frequencies) are being increasingly used in fluorescence, namely in lifetime imaging microscopy (FLIM). In this work, a detailed study of the sum of two exponentials decay function is carried out revealing that sub-exponential, super-exponential and unimodal decays have different phasor signatures. A generalization of the lever rule is obtained, and the existence of an outermost phasor curve corresponding to intermediate-like decays is demonstrated. A study of the behavior of more complex decay functions (sum of three exponentials, stretched and compressed exponentials, phosphorescence with reabsorption and triplet-triplet annihilation, fluorescence with quantum beats) allows concluding that a rich diversity of phasor plot patterns exists. In particular, super-exponential decays can present complex shapes, spiraling at high frequencies. The concept of virtual phasor is also introduced.