Representations of the deformed oscillator algebra under different choices of generators

We discuss from unique position different variants of the commutation relations of the algebra of the $q$-deformed boson oscillator related to the different choices of generators. We consider the generalised form of the commutation relations which include as particular cases all of the most popular variants of such relations. By more or less standard way we describe the methods of construction and classification of the representations of the $q$-deformed oscillator algebra under different choices of generators. We also discuss the possibility of introduction the Hopf algebra structure in this algebra. The possibility of construction of the universal ${\mathscr R}$-matrix for considered algebra are also briefly discussed.