The past two decades have witnessed a tremendous number of computational predictions of hydride-based (phonon-mediated) superconductors, mostly at extremely high pressures, i.e., hundreds of gigapascals. These discoveries were strongly driven by Migdal−E ́liashberg theory (and its first-principles computational implementations) for electron−phonon interactions, the key concept of phonon-mediated superconductivity. Dozens of predictions were experimentally synthesized and characterized, triggering not only enormous excitement in the community but also some debates. In this work, we review the computationally driven discoveries and the recent developments in the field from various essential aspects, including the theoretically based, computationally based, and, specifically, artificial intelligence/machine learning (AI/ML)-based approaches emerging within the paradigm of materials informatics. While challenges and critical gaps can be found in all of these approaches, AI/ML efforts specifically remain in their infancy for good reasons. However, there are opportunities in which these approaches can be further developed and integrated in concerted efforts, in which AI/ML approaches could play more important roles.