Were ancient proteins systematically different than modern proteins? The answer to this question is profoundly important, shaping how we understand the origins of protein biochemical, biophysical, and functional properties. Ancestral sequence reconstruction (ASR), a phylogenetic approach to infer the sequences of ancestral proteins, may reveal such trends. We discuss two proposed trends: a transition from higher to lower thermostability and a tendency for proteins to acquire higher specificity over time. We review the evidence for elevated ancestral thermostability and discuss its possible origins in a changing environmental temperature and/or reconstruction bias. We also conclude that there is, as yet, insufficient data to support a trend from promiscuity to specificity. Finally, we propose future work to understand these proposed evolutionary trends.