A holonomic knot is an embedding C : S1 → R3 which is of the form C(t) = (f(t), f′(t), f′′(t)), where f : S1 → R is a smooth function. Victor Vassiliev showed in his paper titled “Holonomic knots and Smale Principles for Multisingularities” that any smooth knot in R3 is isotopic to a holonomic one. This theorem has two proofs, one using Reidemeister moves and the other using a braid theoretic framework, in conjunction with contributions by Garside. We give a detailed exposition of both methods, while also providing a demonstration with examples. A key ingredient in the proofs is a collection of conditions that are shown to characterize the knot diagrams of holonomic knots.