Some 50 years after at the turn of the 20th century, when Henri Poincaré revealed the unpredictability of solutions to the 3-body problem of celestial mechanics, the new field of nonlinear dynamics was born. This was mainly due to the Kolmogorov-Arnold-Moser (KAM) theory, which established that the opposite is also true, i.e. that many body systems can also exhibit generically stable and predictable behavior. Subsequently, in the 1960’s and 1970’s, chaos was added as a principal component of the dynamics of nonlinear systems. Afterwards, in the 1980’s and 1990’s, another new field called complexity was born to tackle multi-dimensional systems in all the fields of sciences. In 2021, the importance of this field was recognized by the Nobel Physics prize, awarded for contributing to the understanding of the evolution of the Earth’s climate. Currently, there is practically no scientific field where complexity has not yet made remarkable advances, from the natural sciences to engineering, computation, medicine and social sciences. In this special session, we aim first to elucidate, through important examples, some of the main contributions of complexity to the physical, medical and engineering sciences, by focusing on some of its major physical and bio-engineering applications. The topics include but are not limited to: