Recently, the shape of a eukaryotic cell receives increasing attention of researchers of nonequilibriumsoftmatter and biophysics in the context of active softmatter. In this talk, I would like to talkabout my two works on the shape of a eukaryotic cell.Firstly, I will talk about our theoretical study on migration of a eukaryotic cell with shape deformation.As for the active motion of living cells, not only the pure mechanical aspect, but also theinformation processing to recognize their external environment plays crucial roles. In this talk, Iwould like to share with you our recent result that the cell shape qualitatively influences migratingdirections of a chemotactic eukaryotic cell via the information processing. This mechanism is consideredto be one of couplings between the shape and motility of a eukaryotic cell.Secondly, I will talk about our theoretical work on the origin of the active contractile behavior of anactin-myosin network. Actin-myosin networks regulate the shape of a eukaryotic cell by producingthe active contractile force , and control cell migration, cytokinesis and tissue morphology. Now,Dr. Salbreux (Max-Planck-Institut für Physik komplexer Systeme) and I are investigating a contractilemechanism of an actin-myosin network due to the rotational degrees of freedom of actin filaments.I would like to explain our theoretical attempt to understand this kind of active contractilebehavior.B. Hu, D. Fuller, W. Loomis, H. Levine and W. Rappel, PRE 81, 031906 (2010). S. Koehler and A. Bausch, PLoS ONE 7, e39869 (2012).