• Base your null models on biologically meaningful null hypotheses, not just computationally convenient math.
• Generative models and simulation can be useful for more complicated models.
• Picking the right model remains more art than science.

Very good connection of math skills and a feeling of biological problems.

The list of advancements include:

• improvement of the homology modelling: one of the issues in template-based modelling of protein structures was that a final model wasn’t closer to the real structure than a template; now we have statistically significant (although very small) improvement thanks to the multi-template based modelling
• fully automated methods are much closer to human predictors than ever: many groups use models from servers as their starting point and usually they don’t improve them that much

I believe that this was possible thanks to the progress that has been made in the area of sequence homology searches. Finding similarity between two sequences well beyond any reasonable identity thresholds is now doable thanks to profile-to-profile comparison, meta-servers (joining predictions from many different methods) or recent hmm-to-hmm algorithms (comparison of Hidden Markov Models). If you can find a suitable template for your protein, the rest is then much easier, isn’t it?

There are of course fields that still need some work. One of these often stirs a lot of discussion: automated assessing of model similarity to the real structure. The current methods have proven their suitability, I definitely agree. However I hope that at some point the protein structure comparison software will refuse to superimpose eight- and ten-stranded beta-barrels or left- and right-handed coiled-coil with a message: “It doesn’t make sense.”