Vortex-induced motions (VIM) of floating structures are very relevant for the design of mooring and riser systems. In the design phase, spar and monocolumn VIM behavior, as well as semisubmersible and tension leg platform flow-induced motions, is studied and evaluated. This paper provides a checklist of topics and evidence from a number of sources to justify the selection that should be considered when designing spars or monocolumn platforms regarding the VIM phenomenon. An overview of the influential aspects of the VIM is presented such as heading, external appendages of the hull, concomitant presence of waves and currents, motion suppressor, draft condition (immersed portion of the hull), and external damping due to the presence of risers. Previous works concerning the VIM studies on spar and monocolumn platforms are also addressed. Whenever possible, the results of experiments from diverse authors on this matter are presented and compared.