Many animals in nature travel in groups either for protection, survival, or endurance. Among these, certain species do so under the burden of aero/hydrodynamic loads, which incites questions as to the significance of the multibody fluid-mediated interactions that are inherent to collective flying/swimming. Prime examples of such creatures are fish, which are commonly seen traveling in highly organized groups of large numbers. Indeed, over the years, there have been numerous attempts to examine hydrodynamic interactions among self-propelled fish-like swimmers. Though many have studied this phenomenon, their motivations have varied from understanding animal behavior to extracting universal fluid dynamical principles and transplanting them into engineering applications. The approaches utilized to carry out these investigations include theoretical and computational analyses, field observations, and experiments using various abstractions of biological fish. Here, we compile representative investigations focused on the collective hydrodynamics of fish-like swimmers. The selected body of works are reviewed in the context of their methodologies and findings, so as to draw parallels, contrast differences, and highlight open questions. Overall, the results of the surveyed studies provide foundational insights into the conditions (such as the relative positioning and synchronization between the members, as well as their swimming kinematics and speed) under which hydrodynamic interactions can lead to efficiency gains and/or group cohesion in two- and three-dimensional scenarios. They also shed some light on the mechanisms responsible for such energetic and stability enhancements in the context of wake-body, wake-wake, and body-body interactions.