It has been 5 years since the data sample from the LHCb detector, the first experiment optimized for heavy-flavor physics studies at a hadronic collider, was completed. These data led to many major discoveries in exotic hadron spectroscopy, which we review in this article. We supplement the experimental results with a selection of phenomenological interpretations. As the upgraded LHCb detector is expected to collect a larger data sample starting in 2024, we also discuss the potential of the LHCb program in exotic hadron physics for the near future and beyond.