Quantum computers, quantum communication systems, and quantum sensors are expected to revolutionize science and technology by exploiting unique properties of quantum systems like superposition and entanglement. Advances in the underlying science have helped identify an ever-broadening set of compelling use cases for these quantum information technologies. Yet, despite experimental advances, translating design concepts to high-performance hardware remains a significant obstacle preventing these technologies from reaching their revolutionary potentials. In mature engineering fields, these kinds of challenges are typically overcome by leveraging first-principles numerical methods that model the underlying physics (e.g., full-wave methods solving Maxwell's equations) so they can be applied uniformly to any device. For quantum information technologies, such numerical methods are only beginning to be created, but there is a significant opportunity for this. Just as electromagnetic (EM) effects impact many classical technologies, a similarity in the hardware platforms for building quantum information technologies is that the interactions of classical and quantum electromagnetic (QEM) fields with atom-like systems used as qubits in these devices play a central role. In this article, we introduce the basic concepts and emerging trends in the field of numerically modeling these effects on conventional computers, which we broadly term "computational quantum electromagnetics (CQEM)". In an effort to keep this article accessible, we have written it assuming the reader has no detailed background in quantum physics and keep our discussion on the broad opportunities and challenges of the computational strategies in this nascent field.