This paper examines the how and the why of nonlinear speech synthesis. It discusses why nonlinear speech synthesis should be considered, reviews the recent history and describes in detail a variety of approaches to the problem. It argues that while modern concatenative speech synthesisers produce speech which is intelligible, however they are very inflexible and often lack a human quality. The paper does not suggest that nonlinear speech synthesisers are ready to replace conventional approaches, but rather that they offer some potential advantages but there is a considerable amount of research still to be carried out.