More and more experiments show that the CCCTC-binding factor (CTCF), a multi-Cys2His2 (mC2H2) zinc finger protein, plays a key role in the spatial organization of chromatin and gene regulation in the nucleus of eukaryotic cells. In this context an important problem is to uncover the underlying mechanism of how CTCF shapes the chromatin structure. In this thesis, models on different scales, from atomistic scale to coarse-grained scale, are studied to better understand the conformational and dynamical properties of both the unbound CTCF and CTCF-DNA complexes. Using homology modeling, an atomistic model of CTCF is constructed to study the conformational properties of unbound mC2H2 zinc finger proteins. To enhance the computing and sampling efficiency an atomistic pivoting algorithm and a mesoscale model for mC2H2 proteins is developed. It is shown that the conformations of unbound mC2H2 proteins, like CTCF, can be explained with a worm-like chain model. For proteins of a few zinc finger, an effective bending constraint favors an extended conformation, which is consistent with experimental findings. A self-avoiding chain model applies only to proteins of more than nine zinc fingers. As a subsequent step, a mesoscale model is designed to study how a mC2H2 zinc finger protein binds to and searches for its target DNA loci. Statistical sequence-dependent interactions between the proteins and DNA are derived. Molecular dynamics simulations of this model reproduce several kinetic properties of mC2H2 zinc finger proteins, such as the rotation coupled sliding, the asymmetrical roles of different zinc fingers and the partial binding partial dangling mode. An application to CTCF in complexes with one of its target DNA duplex shows that CTCF binds to DNA only by using its central zinc fingers. It asymmetrically bends the DNA duplex but does not form DNA loops. Other CTCF-assisted DNA looping mechanisms, like a bridged DNA loop organized by a CTCF homodimer, could be further studied with this model. Motivated by the non-covalent binding of polypeptides to DNA, I study the adsorption of a flexible polymer to a rigid polymer with periodic binding sites, both in 2d and in 3d. Analysis of Monte Carlo simulation results show that the phase transition, from non-adsorbed to adsorbed with increasing adsorbing strength, is a second order transition in 2d, and higher order transition in 3d. Compared to the adsorbed monomers, successive non-adsorbed monomers contribute more to the winding of the flexible polymer around a rigid polymer, showing the importance of the linkers in mC2H2 zinc finger proteins to wrap around DNA.