Book excerpt: Polarization is a vector nature of light that plays an important role in optical science and engineering. While existing textbook treatments of light assume beams with spatially homogeneous polarization, there is an increasing interest in vectorial optical fields with spatially engineered states of polarization. New effects and phenomena have been predicted and observed for light beams with these unconventional polarization states. This edited review volume aims to provide a comprehensive overview and summarize the latest developments in this important emerging field of optics. This book will cover the fundamentals including mathematical and physical descriptions, experimental generation, manipulation, focusing, propagation, and the applications of the engineered vectorial optical fields in focal field engineering, plasmonic focusing and optical antenna, single molecular imaging, optical tweezers/trapping, as well as optical measurements and instrumentations.