Sound synthesis and processing has been the most active research topic in the field of sound and music computing for more than 40 years. Quite a number of the early research results are now standard components of many audio and music devices and new technologies are continuously being developed and integrated into new products. Through the years there have been important changes. For example, most of the abstract algorithms that were the focus of work in the 70s and 80s are considered obsolete. Then the 1990s saw the emergence of computational approaches that aimed either at capturing the characteristics of a sound source, known as physical models, or at capturing the perceptual characteristics of the sound signal, generally referred to as spectral or signal models. More recent trends include the combination of physical and spectral models and the corpus-based concatenative methods. But the field faces major challenges that might revolutionize the standard paradigms and applications of sound synthesis. In this article, we will first place the sound synthesis topic within its research context, then we will highlight some of the current trends, and finally we will attempt to identify some challenges for the future.