Beginning with a brief review, we will continue discussing the "least prime ideal" problem related to the Chebotarev Density Theorem -- a result concerned with the distribution of prime ideals in number fields according to their splitting behaviour. We will examine two unconditional results due to Lagarias-Montgomery-Odlyzko and Weiss, compare these estimates in some examples, and discuss recent progress towards explicit bounds. The latter work is joint with Jesse Thorner.