Several fold recognition algorithms are compared to each other in terms of prediction accuracy and significance. It is shown that on standard benchmarks, hybrid methods, which combine scoring based on sequence-sequence and sequence-structure matching, surpass both sequence and threading methods in the number of accurate predictions. However, the sequence similarity contributes most to the prediction accuracy. This strongly argues that most examples of apparently nonhomologous proteins with similar folds are actually related by evolution. While disappointing from the perspective of the fundamental understanding of protein folding, this adds a new significance to fold recognition methods as a possible first step in function prediction. Despite hybrid methods being more accurate at fold prediction than either the sequence or threading methods, each of the methods is correct in some cases where others have failed. This partly reflects a different perspective on sequence/structure relationship embedded in various methods. To combine predictions from different methods, estimates of significance of predictions are made for all methods. With the help of such estimates, it is possible to develop a "jury" method, which has accuracy higher than any of the single methods. Finally, building full three-dimensional models for all top predictions helps to eliminate possible false positives where alignments, which are optimal in the one-dimensional sequences, lead to unsolvable sterical conflicts for the full three-dimensional models.