The paper deals with the “centenarian” Heun’s equation in the complex domain: (1)
Firstly, the author recalls the classification of the special cases of Heun’s equations and other basic notions, as a spectrum of Heun’s equation and Heun’s functions. Further, by the properties of the solution of (1), the spectrum of Heun’s equation is characterized. For example, iff the equation (1) has such a solution , for which is a rational function. With help of the Heun’s surface function, the properties of the spectrum are studied. Finally, the WKB-estimates of the solutions of (1) are derived.