Let A be a set of natural numbers. Recent work has suggested a strong link between the additive energy of A (the number of solutions to \(a_1 + a_2 = a_3 + a_4\) with \(a_i\in A\)) and the metric Poissonian property, which is a fine-scale equidistribution property for dilates of A modulo 1. There appears to be reasonable evidence to speculate a sharp Khintchine-type threshold, that is, to speculate that the metric Poissonian property should be completely determined by whether or not a certain sum of additive energies is convergent or divergent. In this talk, I will discuss the history of the metric Poissonian property and its connection to additive energy. I will then present some results related to the convergence theory, that is, the extent to which having a low additive energy forces a set to be metric Poissonian.