Optimal design of structures, or rather just of simple structural elements working under creep conditions, belongs to the most recent branches of structural optimization. It was initiated by four papers published in the years 1967-1968 (Reitman, Prager, Nemirovsky, and Życzkowski). The most important differences with respect to elastic design are as follows: factor of time appearing in the constraints, a great variety of constitutive equations of creep or viscoplasticity, creep rupture hypotheses, creep buckling theories, various definitions of creep stiffness, etc. Moreover, the constraints related to stress-relaxation are quite new. So, it is almost impossible to establish a sufficiently general theory, and various types of problems must be treated separately by appropriate methods. On the other hand, the problems of optimization under creep conditions are important in view of metal structures working at elevated temperatures, structures made of plastics, concrete, etc. This review article gives a classification of problems and then a review of results obtained for bars, columns, arches, trusses, frames, plates, and shells. Over thirty percent of these results were obtained at the Cracow University of Technology. This is an extended and updated version of an earlier review article published in AMR41 (12), December, 1988, discusses specific features of the branch of optimal structural design under consideration, as well as perspectives for future research. This review article contains 187 references.