We investigate the degree of approximation of a \(2\pi \) -periodic function that changes its monotonicity or its convexity finitely many times in its period, by trigonometric polynomials that follows the monotonicity, respectively the convexity of the function everywhere. Such trigonometric functions are said to be comonotone, respectively coconvex with the function. This type of approximation is called Shape Preserving Approximation (SPA). This is a survey about the validity of Jackson-type estimates in uniform SPA of \(2\pi \) -periodic functions by trigonometric polynomials. It is interesting to point out that while the results for coconvex approximation are the same as the analogous results for coconvex approximation, by algebraic polynomials, of a continuous function on a finite interval, the results for comonotone approximation of a periodic function are substantially different than the analogous results for comonotone approximation, by algebraic polynomials, of a continuous function on a finite interval. Finally, we apply the estimates to compare the degrees of unconstrained and shape preserving approximations.