This book covers recent developments in the non-standard asymptotics of the mathematical narrow escape problem in stochastic theory, as well as applications of the narrow escape problem in cell biology. The first part of the book concentrates on mathematical methods, including advanced asymptotic methods in partial equations, and is aimed primarily at applied mathematicians and theoretical physicists who are interested in biological applications. The second part of the book is intended for computational biologists, theoretical chemists, biochemists, biophysicists, and physiologists. It includes a summary of output formulas from the mathematical portion of the book and concentrates on their applications in modeling specific problems in theoretical molecular and cellular biology. Critical biological processes, such as synaptic plasticity and transmission, activation of genes by transcription factors, or double-strained DNA break repair, are controlled by diffusion in structures that have