This is a rather biased review paper emphasizing the importance of “understanding” of phenomena. This paper's purpose is to inspire young researchers to taste the real charms of research by observing the process of development of mathematical models of vortex‐induced vibration phenomena of cylinders for understanding their essential mechanism. It first discusses the limitations of human abilities and important aspects of research. Then, it emphasizes the close relation between understanding and mathematical models, and five conditions for a desirable mathematical model: simplicity; inclusion of all essential properties; possession of physical meanings; wide scope of application; and possibility of development. It refers to Birkhoff's wake‐oscillator (1953), Funakawa's early‐wake model (1969), Nakamura's 2DOF flutter model (1970), the Hartlen‐Currie model (1970), the Iwan‐Blevins model (1974), Tamura's non‐linear wake‐oscillator model with a variable length (1979), and the Tamura–Shimada model (1987) for combined effects of vortex resonance and galloping. Some recent developments of the Tamura–Shimada model are also introduced. Then, it discusses the necessity of accurate experimental capture of early‐wake behavior and the aerodynamic properties of a target cylinder in a given flow condition for further development of Tamura's model and the Tamura–Shimada model. Finally, the necessity for efforts to understand phenomena are emphasized.

Tall buildings have been traditionally designed to be symmetric rectangular, triangular or circular in plan, in order to avoid excessive seismic-induced torsional vibrations due to eccentricity, especially in seismic prone regions like Japan. However, recent tall building design has been released from the spell of compulsory symmetric shape design, and free-style design is increasing. This is mainly due to architects' and structural designers' challenging demands for novel and unconventional expressions. Development of computer aided analytical techniques and of vibration control techniques using auxiliary devices has also contributed to this trend. Another important aspect is that rather complicated sectional shapes are basically good with regard to aerodynamic properties for crosswind responses, which is a key issue in tall-building wind-resistant design. A series of wind tunnel tests have been carried out to determine wind forces and wind pressures acting on 31 tall building models with various configurations: square plan, rectangular plan, elliptic plan, with corner cut, with corner chamfered, tilted, tapered, inverse tapered, with setbacks, helical, openings and so on. Dynamic wind-induced response analyses of these models have also been conducted. The results of these tests have led to comprehensive discussions on the aerodynamic characteristics of various tall building configurations, and studies on corresponding optimal structural systems.