An overview of implicit and explicit phase field models for quasi-static failure processes, implementation and computational efficiency

•An overview of explicit and implicit phase field models details about their theories and implementation is presented.•A comprehensive comparation of the computational efficiency is made between the implicit and explicit phase field models.•Codes associated with the ABAQUS implementation through UEL/VUEL are provided.•A mass/viscosity scaling scheme for the explicit phase field model is presented to increase the critical stable time increment.•A non-iteration scheme for the implicit phase field model is introduced to eliminate the iteration.