Dr. Ioannis A. Kougioumtzoglou is an Associate Professor, Department of Civil Engineering and Engineering Mechanics, Columbia University, NY; Dr. Apostolos F. Psaros is a Post-Doctoral Researcher, Department of Civil Engineering and Engineering Mechanics, Columbia University, NY; and Dr. Pol D. Spanos is the L. B. Ryon Professor in Mechanical and Civil Engineering, Rice University, Texas, USA

• Introduction.- Wiener path integral formalism.- Linearsystems under Gaussian white noise excitation: exact closed form solutions.- Nonlinearsystems under Gaussian white noise excitation.- Nonlinear systems undernon-white, non-Gaussian and non-stationary excitation.- Nonlinear systems with singulardiffusion matrices: a broad perspective including hysteresis modeling.- High-dimensionalnonlinear systems: circumventing the curse of dimensionality via areduced-order formulation.- Efficient numerical implementation strategies viasparse representations and compressive sampling.- An enhanced quadratic Wienerpath integral approximation with applications to nonlinear system reliabilityassessment.- Epilogue.