Astrometric observations tell us that the matter content of the Universe is dominated by dark matter, a quantity that finds no explanation within the Standard Model of particle interactions. Moreover, popular theories that would explain dark matter in terms of new, high-energy physics have as yet no empirical support from studies at high energy colliders. It is possible, rather, that essential clues as to its nature may first come from the appearance of light, weakly coupled new physics, to which low-energy, precision tests of the Standard Model are exquisitely sensitive. In this context, I will discuss an experimental anomaly in $^8$Be nuclear transitions that may be interpreted as evidence for a new, weak force of some 12 fm in range. I will review the experimental evidence, its interpretation and implications, and emphasize what further experimental tests can be done to probe the experimental anomaly and its interpretation.