Traditional casting processes operate at low cooling rates, which are well described by the classic sharp interface model (SIM). The SIM assumes zero interface width, and that the interface is in near-equilibrium during solidification. Phase field modelling of solidification is often done in the binary alloy limit because it is simple in form and yet contains many physical processes found in more complex alloys. The equilibrium conditions that prevail in the classic SIM break down during rapid solidification. The time scale of atomic attachment starts to approach the time scale for diffusion through the interface, invalidating the use of the classic SIM limit. Rapid solidification is becoming the norm in emerging technologies that collectively fit under the banner of “additive manufacturing”. The connection between the phase field model and continuous growth model parameters is non-trivial to derive mathematically, making it difficult to perform quantitative simulations of rapid solidification.