A hypernucleus, a subatomic bound system with at least one hyperon, is a great test ground to investigate nuclear forces and general baryonic interactions with up, down and strange quarks. Hypernuclei have been extensively studied for almost seven decades in reactions involving cosmic rays and with accelerator beams. In recent years, experimental studies of hypernuclei have entered a new stage using energetic collisions of heavy-ion beams. However, these investigations have revealed two puzzling results related to the lightest three-body hypernuclear system, the so-called hypertriton, and the unexpected existence of a bound state of two neutrons with a Λ hyperon. Solving these puzzles will not only impact our understanding of the fundamental baryonic interactions with strange quarks but also of the nature of the deep interior of neutron stars. In this Perspective, we discuss approaches to solving these puzzles, including experiments with heavy-ion beams and the analysis of nuclear emulsions using state-of-the-art technologies. We summarize ongoing projects and experiments at various facilities worldwide and outline future perspectives.