In this talk I will give a broad presentation of my research interests which are in the interplay of modeling, analysis and numerical treatment of Partial Differential Equations (PDEs) describing collective and emerging behavior of phenomena with a possible enormous impact on society, applications and engineering community. For instance, this is the case of traffic flow models, clustering and data flow problems, etc. Mathematical models provide an elegant and robust tool to give important contributions in this direction. My work is mostly based on kinetic and macroscopic scale models which can be formally and rigorously derived from microscopic considerations in a multiscale paradigm, e.g. via mean-field limits and asymptotic or hydrodynamic limits. The typical integro-differential setting and the large phase space associated with a kinetic equation, coupled with the necessity of computing high-order accuracy solutions and handling the stiffness of collision kernels, make the numerical treatment of kinetic and hydrodynamic models another key and challenging aspect of my research. My expertise concerns in particular the study and the analysis of high-order finite volume schemes.