This volume consists of papers written by eminent scientists from the international mathematical community, who present the recent research concerning the problem of Plateau after its classical solution by Jesse Douglas and Tibor Rado. The contributing papers provide insight and perspective on various problems in modern topics of calculus of variations, global differential geometry and global nonlinear analysis as related to the problem of plateau The Linear Stability of Gortler Vortices Revisited / A. Bottaro and P. Luchini -- The Sequence-of-Bifurcations Approach Towards an Understanding of Complex Flows / F. H. Busse and R. M. Clever -- Derivation and Simulations of Evolution Equations of Wavy Film Flows / A. L. Frenkel and K. Indireshkumar -- Instabilities due to Soret Diffusion Coupled to the Morphology of a Solid-Liquid Interface / L. Hadji -- The Instability of Finite Amplitude Waves in Strong Viscid and Inviscid Shear / W. R. C. Phillips -- Nonlinear Stability Analysis and Modeling for Convective Flows / D. N. Riahi -- Modeling and Simulation for Primary Instabilities in Shear Flows / D. N. Riahi -- Gortler Vortices with System Rotation / A. Zebib, A. Bottaro and B. G. B. Klingmann