This thesis explores a wide array of topics related to the protein folding problem, ranging from the folding mechanism, ab initio structure prediction and protein design, to the mechanism of protein functional evolution, using multi-scale approaches. To investigate the role of native topology on folding mechanism, the native topology is dissected into non-local and local contacts. The number of non-local contacts and non-local contact orders are both negatively correlated with folding rates, suggesting that the non-local contacts dominate the barrier-crossing process. However, local contact orders show positive correlation with folding rates, indicating the role of a diffusive search in the denatured basin. Additionally, the folding rate distribution of E. coli and Yeast proteomes are predicted from native topology. The distribution is fitted well by a diffusion-drift population model and also directly compared with experimentally measured half life. The results indicate that proteome folding kinetics is limited by protein half life. The crucial role of local contacts in protein folding is further explored by the simulations of WW domains using Zipping and Assembly Method. The correct formation of N-terminal β-turn turns out important for the folding of WW domains. A classification model based on contact probabilities of five critical local contacts is constructed to predict the foldability of WW domains with 81% accuracy. By introducing mutations to stabilize those critical local contacts, a new protein design approach is developed to re-design the unfoldable WW domains and make them foldable. After folding, proteins exhibit inherent conformational dynamics to be functional. Using molecular dynamics simulations in conjunction with Perturbation Response Scanning, it is demonstrated that the divergence of functions can occur through the modification of conformational dynamics within existing fold for β-lactmases and GFP-like proteins: i) the modern TEM-1 lactamase shows a comparatively rigid active-site region, likely reflecting adaptation for efficient degradation of a specific substrate, while the resurrected ancient lactamases indicate enhanced active-site flexibility, which likely allows for the binding and subsequent degradation of different antibiotic molecules; ii) the chromophore and attached peptides of photocoversion-competent GFP-like protein exhibits higher flexibility than the photocoversion-incompetent one, consistent with the evolution of photocoversion capacity.