Isogeometric Analysis (IGA) is a successful simulation framework originally proposed by T.J.R. Hughes et al., in 2005, with the aim of bridging Computational Mechanics and Computer Aided Design. In addition to this, thanks to the high-regularity properties of its basis functions, IGA has shown a better accuracy per degree-of-freedom and an enhanced robustness with respect to standard finite elements in many applications - ranging from solids and structures to fluids, as well as to different kinds of coupled problems - opening also the door for the approximation in primal form of higher-order partial differential equations.

After a concise introduction of the basic isogeometric concepts, this lecture aims at presenting some IGA recent advances with an overview of a number of interesting applications in different fields like Mechanical, Civil, and Biomedical Engineering. Particular focus will be placed on modeling and simulation of shell structures, dealing also with topics like laminated composites, phase-field fracture, and fluid-structure interaction.