Contents: Introduction to Bezier and spline curves; Interpolation, shape control and shape properties; Shape properties of normalised totally positive bases; Bases with optimal shape preserving properties; Stability and error analysis of shape preserving representations; Blossoming and CAGD algorithms; A geometric approach to variation diminishing free-form curve schemes; Multivariate Bernstein polynomials, convexity and related shape properties; Shape properties of tensor-product Bernstein polynomials; Techniques for fair and shape-preserving surface fitting with tensor-product B-splines; Trigonometric B-basis for defining curves and surfaces; Trigonometric splines; a survey with new results.