CASP15 (2022) showed enormous progress in modeling multimolecular protein complexes.
The assembly modeling (a.k.a. quaternary structure modeling, oligomeric modeling, multimeric modeling) has been assessed in CASP since 2016 (CASP12). Typically, models were of good accuracy when templates were available for the structure of the whole target complex. After the success of AlphaFold2 in CASP14 (2020), it was expected that deep learning methodology that brought monomeric modeling to qualitatively new level will be extended to multimeric modeling. Indeed, CASP15 showed that newly developed methods are capable of accurate reproducing structures of oligomeric complexes and outperform CASP14 methods by a large margin. In particular, the accuracy of models almost doubled in terms of the Interface Contact Score (ICS a.k.a. F1) and increased by 1/3 in terms of the overall fold similarity score LDDTo (left panel). An impressive example of multimeric modeling is shown in the right panel below.

CASP14 marked an extraordinary increase in the accuracy of the computed three-dimensional protein structures with the emergence of the advanced deep learning method AlphaFold2. Models built with this method proved to be competitive with the experimental accuracy (GDT_TS>90) for ~2/3 of the targets and of high accuracy (GDT_TS>80) for almost 90% of the targets (middle plot). The accuracy of CASP14 models for TBM targets significally superseeded accuracy of models that can be built by simple transcription of information from templates, and reached the level of GDT_TS=92 on average, which is significantly higher than the corresponding averages in previous two CASPs (right plot).

CASP14 marked an extraordinary increase in the accuracy of the computed three-dimensional protein structures with the emergence of the advanced deep learning method AlphaFold2. The CASP14 trend line in the historical progress plot (panel 2, black trendline) starts at a GDT_TS of about 95, and finishes at about 85 for difficult targets. Because of experimental errors and artifacts, a GDT_TS of 100 is highly unlikely. In CASP14, about 2/3 of the 96 targets reached GDT_TS values greater than that, and so are considered competitive with experiment in backbone accuracy.

The most notable progress in recent CASPs (2014, 2016) resulted from sustained improvement in methods for predicting three-dimensional contacts between pairs of residues in structures. Average precision of the best CASP12 contact predictor almost doubled compared to that of the best CASP11 predictor (from 27% to 47% - see the plot). Advances in the field as a whole are not any less impressive: 26 methods in CASP12 showed better results than the best method in CASP11. [Schaarschmidt et al, 2018]
Theoretical advance in contact prediction lead to improved accuracy of 3D models, especially for the hardest template-free modeling cases (see models for CASP12 target T0915 below).
CASP13 (2018) registered yet another leap in accuracy of contact prediction, with the average precision of the best contact prediction group increasing by 23% (compared to CASP12) and reaching 70%. There has been no noticeable increase in the accuracy of predicted contacts between CASP13 and CASP14 (left graph).

In early CASPs, generated models have occasionally helped solve structures. For example, the crystal structure of Sla2 ANTH domain of Chaetomium thermophilum (CASP11 target T0839 - see the image below) was determined by molecular replacement using CASP models, but these have been exceptions.

In CASP14, four structures were solved with the aid of AlphaFold2 models. A post- CASP analysis has shown that models from other groups would also have been effective in some cases. These are all hard targets with limited or no homology information available for at least some domains, demonstrating the power of the new methods for all classes of modeling difficulty. For one other target, provision of the models resulted in correction of a local experimental error. A detailed account of these cases is provided in the Proteins paper [Kryshtafovych et al, 2021]

Refinement category assesses ability of methods to refine available models towards a more accurate representation of the experimental structure. CASP10-14 assessments showed two trends in methods development. First, some molecular dynamics methods can consistently even though very modestly improve over the starting models. A group of more aggressive refinement methods showed to be able to provide very impressive examples of substantial improvement, though at the price of consistency (occasionally models move away from the experimental structure rather than towards it).
Below is are some examples of notable refinement in CASP12. The target structure is shown in orange, the starting model in green and the refined model in blue. [Hovan et al, 2018]

Data-assisted or hybrid modeling, in which low-resolution experimental data are combined with computational methods, is becoming increasing important for a range of experimental data, including NMR, chemical cross-linking and surface labeling, X-ray and neutron scattering, electron microscopy and FRET. CASP11-CASP13 experiments included a special sub-category of modeling proteins using such data (CASP14 did not include data-assisted category due to the COVID-19-associated difficulties in obtaining experimental data).
Description of the CASP12 data-assisted experiment and the data is provided in [Ogorzalek et al, 2018]
Examples of a non-assisted model and a cross-linking assisted model from the same predictor (CASP12 group 220) are shown below demonstrating increased accuracy of the assisted prediction.