The computational modeling of protein structures has become an essential approach for studying biological systems in atomistic detail as an alternative to experimental structure determination methods. As the number of experimentally determined protein structures keeps growing, protein structure prediction based on homologous structures has become more widely applicable and reliable. At the same time, the growth in structures as well as the rapid growth in sequence databases has enabled accurate predictions based on predicted inter-residue distances. Such distance information can be inferred from co-evolutionary couplings , especially via deep neural network models that take advantage of recent progress with machinelearning techniques. This approach has been groundbreaking, especially for protein sequences for which close homolog structures have not yet been determined. Using either approach, it is now possible to predict protein structures from their primary sequence with reasonable accuracy in most cases. However, predicted structures still need to be optimized further to reach experimental accuracy as minor structural differences resulting from variations in the primary sequences are most difficult to capture with knowledgedriven techniques. Models generated by template-based modeling by construction resemble the structures of the templates. These models are expected to be similar to the structure for a homologous target sequence when the degree of sequence identity is high, but such template-based models cannot usually capture how sequence variations may modulate the structure in detail. Because of differences in sidechains, homology models may have poor structure packing. Also, models can be incorrectly predicted in some regions if the sequences are very distant from the sequence of the modeling templates and/or when sequence alignments do not optimally reflect structural equivalency of residues in homologous structures. On the other hand, models based on machine-learning methods may also deviate from their native structures, since current machine learning-based methods rely on co-evolutionary analysis of many close sequence homologs. Thus, the predicted contacts essentially focus on the average structure of an ensemble of a homologous set of sequences, rather than individual structural deviations of a given target sequence.