While science continues to extend to two extremes - micro-scale towards dimensions even smaller than elemental particles and mega-scale even beyond the universe, one recognizes that reductionism is not sufficient to solve many problems we encounter in engineering, which are likely characterized by nonlinearity, nonequilibrium and dissipative multi-scale structures. On the other hand, the common features of these nonlinear systems, such as bifurcation, state multiplicity and self-organization, have attracted much attention, leading to the approaches of the so-called complexity science which has become a focus not only in natural science and engineering science, but also in social science. However, no effective methodology has been established to understand these complex systems, though noticeable progress has been achieved in studying these systems, such as particle-fluid multi-phase systems. Multi-scale methodology has been considered as a promising methodology to tackle complex systems due to its capability in correlating phenomena at different scales. In this presentation, we shall review the development of the multi-scale methodology and its applications to particle-fluid systems, elucidating the essential relevance of complex systems and the challenging problems in chemical engineering. Multi-scale structure is considered to be the focus in studying complex systems, particularly, correlation between phenomena at different scales, compromise between different dominant mechanisms, coupling between spatial and temporal structural changes and critical phenomena occurring in these systems - these are the four critical issues in understanding complex systems. We first propose that by analyzing particle-fluid systems complex systems can be formulated as a multi-objective variational problem. Such an analytical multi-scale method will be reviewed in particular by analyzing the above four critical issues and by showing its 20-year development at IPE from a rough idea to modeling approaches, softwares and finally to industrial applications as well as its extension to different chemical and physical systems. The strategy of “from the particular to the general” in developing this multi-scale methodology is emphasized and challenges to mathematicians and physicists are identified to show the necessity of transdisciplinary cooperation. This presentation will be concluded by prospects and suggestions. While science continues to extend to two extremes - micro-scale towards dimensions even smaller than elemental particles and mega-scale even beyond the universe, one recognizes that reductionism is not sufficient to solve many problems we encounter in engineering, which are likely characterized by nonlinearity On the other hand, the common features of these nonlinear systems, such as bifurcation, state multiplicity and self-organization, have much attention, leading to the approaches of the so-called complexity science has become a focus not only in natural science and engineering science, but also in social science. However, no effective methodology has been established to understand these complex systems, though noticeable progress has been achieved in studying these systems, such as particle-fluid multi -phase systems. Multi-scale methodology has been considered as a promising methodology to tackle complex system s due to its capability in correlating phenomena at different scales. In this presentation, we shall review the development of the multi-scale methodology and its applications to particle-fluid systems, elucidating the essential relevance of complex systems and the challenging problems in chemical engineering Multi-scale structure is considered to be the focus in studying complex systems, particularly, correlation between phenomena at different scales, compromise between different dominant mechanisms, coupling between spatial and temporal structural changes and critical phenomena occurring in these systems - these are the four critical issues in understanding complex systems. We first propose that by analyzing particle-fluid systems complex systems can be formulated as a multi-objective variational problem. Such an analytical multi-scale method will be reviewed by the above four critical issues and by showing its 20-year development at IPE from a rough idea tomodeling approaches, softwares and finally to industrial applications as well as its extension to different chemical and physical systems. The strategy of “from the particular to the general ” in developing this multi-scale methodology is emphasized and challenges to mathematicians and physicists are identified to show the necessity of transdisciplinary cooperation. This presentation will be concluded by prospects and suggestions.