Nonlinear Model Predictive Control (NMPC) formulations through quasi-Linear Parameter Varying (qLPV) embeddings have been brought to focus in recent literature. The qLPV realisation of the nonlinear dynamics yields linear predictions at each sampling instant. Thereby, these control strategies offer online implementation with numerical toughness of Sequential Quadratic Programs (SQPs), which can be solved much faster than the Nonlinear Programs (NPs) generated with "regular" NMPC design. The general lines of such methods are as follows: (i) The qLPV embedding is formulated with state-dependent scheduling parameters; (ii) recursive extrapolation procedures are used to estimate the values of these parameters along the prediction horizon; (iii) these estimates are used to compute linear predictions, which are used to compute the control law through a constrained optimisation procedure. This paper details the overall concept of these novel NMPC techniques and reviews two different (efficient) implementation options. Realistic academic examples are also provided, considering a suspension system and a cascaded tank process.