Zernike circle polynomials are in widespread use for wavefront analysis in optical design and testing. We discuss why we use these polynomials in optics, when to use them, and when not to. Because of their orthogonality over a circular disc, when a circular wavefront is expanded in terms of them, the value of an expansion coefficient is independent of the number of polynomials used in the expansion. We start with the aberrations of a rotationally symmetric imaging system, introduce Strehl ratio, discuss aberration balancing, and thereby justify the use of Zernike circle polynomials. We illustrate the pitfalls of using Zernike polynomials for analyzing a noncircular wavefront by considering a system with an annular pupil. Finally, we show how to obtain the Zernike coefficients when the data available is not the wavefront, but its slope or curvature.