Predicting the structure of a protein from its amino acid sequence is a long-standing unsolved problem in computational biology. Its solution would be of both fundamental and practical importance as the gap between the number of known sequences and the number of experimentally solved structures widens rapidly. Currently, the most successful approaches are based on fragment/template reassembly. Lacking progress in template-free structure prediction calls for novel ideas and approaches. This article reviews trends in the development of physical and specific knowledge-based energy functions as well as sampling techniques for fragment-free structure prediction. Recent physical- and knowledge-based studies demonstrated that it is possible to sample and predict highly accurate protein structures without borrowing native fragments from known protein structures. These emerging approaches with fully flexible sampling have the potential to move the field forward.