In chemistry, as in any other branches of science, experiments often, precedes theory. d. And radical chemistry is no exception. It is therefore perhaps useful to outline, in the very broad manner, the way the field developed over the past century or so, viewed from the perspective of the synthetic organic chemist. Recently the role of free radicals in health has attracted tremendous interest in the field of medicine, dentistry and molecular biology. There currently exists a wide range of degradable polymers that hold potential as biomaterials. Hydrogels are a class of materials which present a three dimensional (3D) structure, consist of hydrophilic polymers and retain a signiﬁcant amount of water. Due to their good biocompatibility, ﬂexibility in fabrication, variable composition, and desirable physical characteristics (similar to physiological conditions), hydrogels alone or combined with cells have many biomedical applications. The objectives of this book is to evaluate the development and influence of free radical synthetically useful transformations and the novel chitosan and β-cyclodextrin bio-polymers as functional designer biomaterials from chemistry to applications.