The interpolation of bilinear operators is a classical problem in interpolation theory. The situation for the real and the complex interpolation methods is well understood. However, few results are known for other interpolation methods. In the paper under review, the author proves new abstract results on interpolation of bilinear operators that involve the minimal and maximal interpolation constructions in the sense of \textit{N. Aronszajn} and \textit{E. Gagliardo} [Ann. Mat. Pura Appl., IV. Ser. 68, 51--117 (1965; Zbl 0195.13102)]. These abstract results give rise to more concrete ones for the Calderón--Lozanovskii method on couples of Banach lattices, and to Musielak--Orlicz spaces. Finally, the author presents applications to the interpolation of couples of spaces of bounded linear operators and a variant of a result of \textit{G. Pisier} [Math. Nachr. 148, 243--245 (1990; Zbl 0735.47026)] concerning an embedding interpolation formula for \((E,p)\)-summing operators with respect to the Gustavsson--Peetre method.