Quantum computing is a technology quickly turning from fantasy to reality. These devices operate on fundamentally different principles from classical computers, but many of the techniques used by computer scientists can be applied to harness the power of quantum computers. This document provides a history of innovation in the field, a mathematical description of how quantum computers work, and analysis of how they are used in today’s world. The information presented is based on textbooks, academic papers, and lecture notes which are all publicly available online. Our society is currently standing on the frontier of new possibilities and quantum computers are one of the keys to unlocking future technological advancements in every field.