Cable-stayed structures are simple in assembling, light in weight, safe in maintenance, and often possess the architectural expressiveness. Today’s cable-stayed structures erected in Germany, France, Italy, Japan, Singapore, USA, South Korea, Australia, and other countries are recognized as unique and innovative structural solutions. Unique first-of-its-kind systems and the well-known structures and buildings of all types, which have practical importance and novelty and were marked by the rewards of professional associations or were passed into the top lists of journals, are presented in the paper. But there is no current classification of cable-stayed structures till present time. New classification of cable-stayed structures containing five groups or ten sub-groups of considered structures is offered. It is impossible to present all meaningful cable-stayed structures in one paper but every sub-group is illustrated by specific notable examples. The principal information on the 90 remarkable cable-stayed public and industrial buildings are submitted for consideration and a special table with the indication of country, architects, and year of erection of these structures was compiled first. The existence of such cable-stayed structures as "suspended bridges" of two types is indicated but their description is not given, because it is the subject of analysis for bridge engineers. The 58 references presented in the manuscript will help to obtain additional information.