This volume consists of eight original survey papers written by invited lecturers in connection with a conference "Variational Methods for Evolving Objects" held at Hokkaido University, Sapporo, Japan, July 30 – August 3, 2012. The topics of papers vary widely from problems in image processing to dynamics of topological defects, and all involve some nonlinear phenomena of current major research interests. These papers are carefully prepared so that they serve as a good starting point of investigation for graduate students and new comers to the field and are strongly recommended.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America