Protein evolution can be studied through models that learn statistical constraints from natural sequence families. These models are often evaluated either as mutation predictors or as generators of natural-like sequences. In this thesis I ask a different question: when a learned protein model is turned into an evolutionary landscape, what kind of long-time sequence exploration does it produce? I compare four models of protein families: Boltzmann-machine Direct Coupling Analysis, asymmetric pseudolikelihood DCA, an autoregressive Transformer, and a masked Transformer. A central part of the work is the development and implementation of evolutionary dynamics for the Transformer-based models, extending the approach that had previously been used for DCA-based landscapes.