Infrared Behavior of Quantum Fields in Inflationary Cosmology -- Issues and Approaches: an overview

This is a pedagogical guide to works on this subject which began in the 80s but has seen vibrant activities in the last decade. It aims to help orient readers, especially students, who wish to enter into research but bewildered by the vast and diverse literature on this subject. We describe the three main veins of activities: the Euclidean zero-mode dominance, the Lorentzian interacting quantum field theory and the classical stochastic field theory approaches in some detail, explaining the underlying physics and the technicalities of each. We show how these approaches are interconnected, and highlight recent papers which contain germs of worthy directions for future developments.