In this talk I shall discuss special polynomials associated with rational solutions for the Painleve equations. The Painleve equations (PI-PVI) are six nonlinear ordinary differential equations that have been the subject of much interest in the past thirty years, which have arisen in a variety of physical applications. Further they may be thought of as nonlinear special functions and arise as symmetry reductions of soliton equations which are solvable by the inverse scattering method, such as the Korteweg-de Vries, Boussinesq and nonlinear Schroedinger equations. Rational solutions of the Painleve equations are expressible in terms of the logarithmic derivative of certain special polynomials. For PII these polynomials are known as the Yablonskii-Vorobev polynomials, first derived in the 1960's by Yablonskii and Vorob'ev. The locations of the roots of these polynomials is shown to have a highly regular triangular structure in the complex plane. The analogous special polynomials associated with rational solutions of PIII, PIV and PV are described and it is shown that their roots also have a highly regular structure.