the four-force
Newton's second law, F = dp/dt, is not yet a relativistic statement because it uses coordinate time t. The four-force is its covariant completion — the rate of change of four-momentum with respect to proper time — so that 'force equals rate of change of momentum' holds as an equation between four-vectors, valid in every inertial frame.
The four-force (Minkowski force) is K^mu = dp^mu/dtau = m A^mu (for constant rest mass), where tau is proper time and A^mu the four-acceleration. Its space components relate to the ordinary Newtonian three-force F by K = gamma F, and its time component is K^0 = gamma (F·v)/c — the rate at which the force does work, i.e. delivers energy. Because p·p = m^2 c^2 is constant for fixed mass, K·U = 0: the four-force is Minkowski-orthogonal to the four-velocity, the covariant statement that a pure force changes direction and energy but not rest mass.
The prime example is electromagnetism: the Lorentz four-force on a charge q is K^mu = (q/c) F^mu_nu U^nu, where F^mu_nu is the electromagnetic field tensor — a single manifestly covariant equation containing both the electric force and the magnetic v x B force. Caveat: K·U = 0 assumes rest mass is constant; if a 'force' also changes the particle's rest mass (it absorbs energy internally, or in a variable-mass problem) the neat orthogonality fails and one must keep both the m U-dot and m-dot U terms.
For a charge in a pure electric field E along x, the spatial four-force is gamma qE and the time component gamma qE v_x/c tracks the power delivered; integrating dp/dtau gives the hyperbolic, ever-slower-in-lab acceleration characteristic of relativistic dynamics.
The four-force unifies the mechanical force and the power it delivers into one four-vector.
Beware two different 'forces': the Minkowski four-force K^mu = dp^mu/dtau and the everyday three-force F = dp/dt differ by a factor of gamma (K = gamma F for the spatial part). They agree only in the low-speed limit gamma -> 1.