We call attention to the readers some short survey of the known iterative algorithms for solving monotone variational inequalities using metric and generalized projection operators in Banach spaces. Beforehand in Sections 1-3, we present the sufficiently full set of the fundamental knowledge (concepts, definitions and facts) necessary in order to prove the succeeding main theorems. At the same time, we omit the proofs themselves and refer the readers to the corresponding papers.

Banach spaces, variational inequalities, uniformly monotone operators, properly monotone operators, explicit iterative algorithms, implicit (proximal) iterative algorithms, metric and generalized projections, Cesàro average approximations, strong and weak convergences, applications.