Double corrugated, self-supporting K-span arch structures are now commonly used globally to make roofs for building structures, as an alternative to traditional solutions. The K-span system has become popular mainly due to the simple and cheap method of its manufacturing and quick installation. Nowadays, new versions of the system are created but still there is no valid design method. Design difficulties are among the causes of failures or even collapses of such structures. Back in the 1970s, the first studies were developed concerning computational analyses of double corrugated arch roofs. They laid grounds for the development of contemporary K-span system technology but have since lost their practical advantages due to changing engineering conditions. The paper presents a review of research and computational methods concerning double corrugated arch structures. The paper discusses selected scientific studies, which were used as the basis for the development of research and computational methods, and their contemporary continuation. Directions for further research and analyses are also presented which could contribute to the future development of science and engineering in the area and could provide inspiration for future studies.