Driven by the ever increasing demand in function integration,more and more next generation high value-added products,such as head-up displays,solar concentrators and intra-ocular-lens,etc.,are designed to possess freeform (i.e.,non-rotational symmetric) surfaces.The toolpath,composed of high density of short linear and circular segments,is generally used in computer numerical control (CNC) systems to machine those products.However,the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration,which will decrease the machining efficiency and product surface finish.Driven by the ever-increasing need for high-speed high-precision machining of those products,many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry,aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods.This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications.The advantages and disadvantages of these approaches are discussed.Possible future research directions are also offered.