This chapter provides an introduction to the MesoBioNano (MBN)Science — a novel field of interdisciplinary research interlinking research areas in Physics, Chemistry, Biology, Materials Science and related industries. It gives a short overview of the major computational approaches exploited in the field with the emphasis on the multiscale computational modelling by means of MBN Explorer — a multi-purpose software package for advanced multiscale simulations of complex molecular structure and dynamics. The chapter presents the unique features of MBN Explorer enabling efficient simulations of structure and dynamics of a large variety of very different complex molecular systems with the sizes ranging from the atomic up to the mesoscopic scales. It introduces the application areas of MBN Explorer and describes MBN Studio-a special multi-task toolkit for MBN Explorer,which enables construction of computational projects, simple start of simulations with MBN Explorer, as well as visualization and analysis of the results obtained.