Over the past few decades there has been a great interest in the analysis of the anomalous transport phenomena that appear in complex biological and nanoscale systems. Several mathematical methods have been proposed but a consistent theory is missing. This book is concerned with the derivation of mathematical billiards that can be proposed as models for the study of the mass transport in microporous media. The book provides the relevant background of the mathematical theory of integrable and chaotic billiards and by employing a case study approach explores the onset of different transport phenomena. This book is addressed to graduate students and applied mathematics researchers involved in the mathematical modeling of the transport phenomena in complex systems.