Of course you probably know that not only time and length change for a moving object, but mass also changes. The first obvious consequence is that only particles with zero rest mass can achieve the speed of light. In accelerating a massive particle, the closer you get to light speed the more massive the particle, and therefore the greater the force required to continue accelerating. At Light speed the mass would be infinite, and thus we say no massive particle can be accelerated to the speed of light. This is not the same as saying nothing can move faster than light.
Physicists call such particles 'tachyons', though there is no evidence for their existence.
Another interesting consequence is that as you continue to add energy to a particle travelling near light speed, the particle stores this energy as an increase of mass rather than an increase in velocity. When they leave, the energy and mass have increased by a factor of more than 6, while their speed has barely changed.