1. Introduction
Scientific research in the 21st century is characterized by research problems of increasing complexity amidst a data revolution. An ever-growing number of scientific research problems are now focused on systems and processes that are complex not only in terms of their underlying mechanisms and governing principles but also by virtue of the high-dimensional and heterogeneous data worlds that they live in. Modeling, simulation, and high-performance computing, alongside experiments, are indispensable for tackling such problems — numerous success stories have been published across diverse fields. Nonetheless, the unabated increases in complexity and data-intensiveness of modern research problems are now posing three evolving challenges for training a new generation of researchers to have the right tools to navigate the emerging challenges. First, many contemporary problems are now defined over multiple length and time scales (i.e., they are multiscale) and also by multiple distinct, yet intricately coupled, physical, chemical and/or biological processes (they are multiphysics). Solving multiscale-multiphysics problems through multiscale modeling (MSM) methods requires the construction of highly sophisticated algorithms at different scales, the rigorous coupling of the scales, and laborious algorithmic implementation using message passing on parallel high-performance computing (HPC) platforms. Second, the associated increases in data types, data intensiveness, and the types of questions asked, now require more sophisticated approaches for data analysis, including machine learning (ML) techniques, which are becoming indispensable in many applications. Third, MSM and ML approaches have evolved independently, and therefore, the art of combining them is very much an emerging paradigm. This review article describes the convergence of several advances in the scientific literature that has made the field of MSM what it is today and provides a perspective of its future, hoping that it would benefit current and potential researchers navigate and advance the field of MSM.