This paper attempts to introduce to the Chinese community of Applied Mathematics and Mechanics the interdisciplinary subject-dendritic pattern formation in solidification. I shall describe the related mathematical issues, which include the free boundary problem, eigenvalue problem, limiting state selection, etc. and summarize the major results achieved during the last decade in terms of a unified, systematic asymptotic approach. These results, exploring the wave-characteristics of interface evolution in dendritic growth, lead to the so-called interfacial wave (IFW) theory.