Successful fold recognition can be readily achieved by current homology detection methods if there exists sufficient sequence similarity between the protein of interest and known structures. However, when such sequence signal does not exist or is too remote to be detected, the task of fold recognition and tertiary structure prediction becomes immensely difficult due to the enormous conformational space to explore. In this thesis, a novel contact threading approach, PhyrePower, which avoids the sequence constraint by identifying structural similarity through protein contact map matching is presented. By combining eigendecomposition and classic dynamic programming algorithms, PhyrePower can effectively utilize the information in predicted residue-residue contacts even in the presence of considerable noise. The potential of this approach is exemplified by its ability to identify a similar structure for 36% of the proteins in a validation set where structural relatives were completely undetectable by the state-of-the-art profile HMM-HMM method. With a simple alignment refinement, a model with a TM-score above 0.5 against the native structure was constructed for 18% of the proteins by PhyrePower. Traditionally, predicted protein contact maps were used as distance constraints in template-free modelling. A widely used molecular mechanics package, TINKER was thoroughly optimised in this work to represent the upper limit on the performance of such contact-assisted methods and a model with a TM-score above 0.5 against the native structure was produced for 11% of the proteins in the validation set. A comparative evaluation between the two methods demonstrated PhyrePower's ability to succeed on the challenging modelling task where an advanced sequence-based method and a direct modelling approach both failed and thus, highlighted PhyrePower's added value in protein folding.