A uniformly accelerated reference frameSis defined as a set of observers who remain at rest with respect to a given observer A who is accelerating at a constant rate with respect to the instantaneously comoving inertial frames. The one‐dimensional uniformly accelerated reference frameSis considered. The world lines of A and the other observers making upSare determined. Coordinates useful for describing events inSare carefully defined and the transformation equations between different sets of them are derived. The variation with position inSof the speed and frequency of light waves is determined. The motion of a free‐particle inSis determined. Various phenomena inS, ordinarily associated with general relativity, are considered, in particular the asymmetric aging of twins at rest at different positions and the existence of horizons.