Polynomial knot theory is similar to holonomic knot theory except that here we have non compact knots. It is well known that every knot-type has a representative given by a polynomial embedding from ${\bf R} $ to ${\bf R}^3$ which is unique up to {\it polynomial isotropy}. We will discuss the motivation behind the polynomial representation of knots and try to see some methods to explicitly construct polynomial representation for few classes of knots.