Predicting a protein's three-dimensional structure from its amino acid sequence was, for five decades, the kind of problem that structural biologists cited as a benchmark of how far computational methods still had to travel. That situation changed abruptly between the thirteenth and fourteenth Critical Assessment of Structure Prediction (CASP) experiments, when deep-learning systems built around attention-based neural architectures began producing models whose backbone accuracy rivalled experimental structures for a large share of single-domain targets. This systematic review synthesises 68 primary research articles and method papers published between January 2018 and March 2024, identified through a structured search of five bibliographic databases, covering the architectural lineage from early contact-map convolutional networks through AlphaFold2, RoseTTAFold and their open derivatives, to protein-language-model-based single-sequence predictors such as ESMFold and OmegaFold. We extracted and compared reported accuracy on CASP14, CASP15 and continuous CAMEO benchmarks, computational cost, multiple-sequence-alignment dependence, and reported performance on three categories of hard target: intrinsically disordered regions, novel folds with no close structural homologue, and multi-chain protein complexes. Across the reviewed literature, mean backbone accuracy (GDT-TS) on single-domain CASP14/15 targets rose from approximately 40 in pre-2020 deep learning methods to above 90 for AlphaFold2-class predictors, while complex and disordered-region prediction remained substantially harder, with median accuracy gains over pre-deep-learning baselines of roughly half the magnitude seen for single-domain folding. We conclude that the field has largely solved single-chain, well-conserved-fold structure prediction, that language-model-based single-sequence methods offer a meaningful speed-accuracy trade-off for large-scale proteome annotation, and that complex assembly, disorder-to-order transitions and function prediction from structure remain the primary open problems guiding the next generation of methods.