Over the course of The Original Series and the first six Star Trek films, numerous models representing the Constitution-class have been created (in particular, for the USS Enterprise), even more than for any other class.
As art director on the original series, Matt Jefferies was given the assignment to design the Enterprise itself. His only guideline was Gene Roddenberry's firm list of what he did not want to see: any rockets, jets, or fire-streams. The starship was not to look like a classic, and thus dated, science-fiction rocket ship, but neither could it resemble anything that would too quickly date the design. Somewhere between the cartoons of the past and the reality of the present, Matt Jefferies was tasked with presenting a futuristic design of his own.
The theory that space could be warped - a hypothetical means of faster-than-light travel - had first been proposed by Albert Einstein in 1905. Years later, Star Trek itself would establish that Zefram Cochrane had first demonstrated warp drive in 2063. In the 1960s, however, warp drive - a delicately balanced, intricate web of chemistry, physics, mathematics and mystery - initially perplexed Matt Jefferies.