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The wavefront aberration for a given field point is often expanded in Zernike polynomials and varies when pupil is modified. In many cases the coefficients pattern corresponding to a pupil is known and one needs to calculate the one for a rotated, contracted or decentred pupil. In this paper we review the most important concepts which we present in recent articles concerning the development of an analytical and a graphical method to carry out this transformation. Using our analytical method we find explicit expressions for the elements of a matrix which transforms Zernike coefficients of up to 7th order computed for a circular original pupil into those corresponding to a contracted, decentred and rotated new pupil. Our graphical method is useful to identify qualitatively new coefficients in terms of original ones or vice versa for any order of Zernike´s expansion. As an example, we show an application of both methods. Finally, we synthesize some works of other authors which develop numerical or analytical methods for the coefficients conversion and we compare their more relevant results to ours.