History-determinism was introduced by Henzinger and Piterman in Solving Games without Determinisation (CSL 2006) as a means to reduce the complexity of reactive synthesis algorithms, and independently discovered by Colcombet in the context of cost functions (The theory of stabilisation monoids and regular cost function, ICALP 2009). At the 32nd Nordic Workshop on Programming Theory (NWPT 2021), I gave a talk to present some preliminary results obtained together with Karoliina Lehtinen about the class of history-deterministic register automata. As of today, this is work in progress, and we hope to understand more about them in the months to come, as they offer promising perspectives to further the study of reactive synthesis over infinite alphabets (see this article for our contribution to this line of reasearch).