Finding the Energy-Momentum Relationship

In classical physics, we can say that if we hold potential energy to be zero, then the total energy of an object is just the same as its kinetic energy. The energy-momentum relationship in classical physics is simply

E = P²/2M.
But, in toto, we're not in classical physics anymore.

Does the old relationship still hold in the relativistic world of high-energy particles? Or must we discover a new relationship?