We formulate the special relativistic generalization of Newtonian projectile motion in three spatial dimensions. Two models are considered: (i) a constant laboratory force, and (ii) a constant proper acceleration, i.e. hyperbolic motion. For the constant-force model we derive closed-form expressions for the coordinates, velocity, four-momentum, energy, and four-force as functions of the laboratory coordinate time. For the constant-proper-acceleration model we derive the worldline parametrized by proper time, together with the four-velocity, fouracceleration, four-momentum, energy, and four-force. We then establish the precise relation between the two models (Sec. 3.6): both have constant proper acceleration, but they describe the same worldline only for one-dimensional motion with matched initial conditions; in general the constant-force model has proper acceleration and a rotating four-acceleration direction. We develop the four-dimensional Lorentz transformation in full generality, including arbitrary-direction boosts, the transformation of time andspatial coordinates, and the transformation of four-vectors. Finally, we demonstrate theLorentz covariance of Maxwell’s equations and of the four-dimensional Lorentz force in manifestlytensor form. In both projectile models the nonrelativistic limit recovers the standardparabolic trajectory. We discuss the relevant conservation laws and emphasize that a truegravitational field requires general relativity, while the present treatment corresponds to auniform external force or a local uniform-field approximation.