Biological systems have both robustness and plasticity, a property that distinguish them from artificial systems and is essential for their survival. Biological systems generally exhibit robustness to various perturbations, including the noise in gene/protein expressions and unexpected environmental changes. At the same time, they are plastic to the surrounding environment, changing their state through processes like adaptation, evolution and cell differentiation. Although the coexistence of robustness and plasticity can be understood as a dynamic property of complex and interacting networks consisting of a large number of components, the mechanisms responsible for the coexistence are largely unknown. Thus, the research aim of our team is to understand these mechanisms in biological systems. We have hypothesized that to maintain robustness and plasticity, there exists an interplay between different hierarchical layers in the systems. For example, in the development of multicellular organisms, plasticity is maintained through a dynamic interplay between the intra-cellular dynamics and cell-cell communications at the cellular state through differentiation, while robustness in the organ/tissue layer is maintained by the regulation of cell growth and differentiation frequency. In another example, we demonstrated by theoretical analysis that fluctuations in gene/protein expression levels and phenotypic plasticity to environmental changes are necessary for robust evolutionary dynamics, indicating that an interplay between cellular dynamics of different time-scales is essential for adaptation and evolution (Kaneko and Furusawa, Jour. Theor. Biol. 2006). In our studies, we focus on the following two topics; i) dynamics of stem cell differentiation and ii) adaptation and evolution in microorganisms. The ultimate goal of our work is to extract the universal features in cellular dynamics that are responsible for robustness and plasticity in biological systems. Despite their complexity, we aim to describe the cellular dynamics using a relatively small number of degrees of freedom with the macroscopic state variables commonly seen in thermodynamics. We expect that such a description will provide a novel method for the prediction and control of complex biological systems.