Abstract: The static and dynamic properties of confined polymer chains are not only of great importance in polymer physics, but also drawing much attention of those researchers in biophysics. The confined polymer chains exhibit a series of unique features as compared with unperturbed polymer chains. At first, by taking the Rouse, Zimm and partially permeable sphere models as examples, this review briefly outlines the fundamental properties of unperturbed polymer chains. Although the Rouse model is the simplest version of the bead-spring model and assumes there are no excluded volume and hydrodynamic interactions between the beads, it can qualitatively describe most of the polymer dynamical behaviors. By taking into account the two-body hydrodynamic interactions between beads, Zimm model successfully obtains the expressions for the diffusion coefficient and the relaxation time that agree with most experimental results of linear polymers. The partially permeable sphere model introduces two phenomenological functions, the drainage function and the drag function, and captures the physical effects due to multibody hydrodynamic interactions at the mean-field level, which provides a simple and unified framework for describing and understanding the intrinsic viscosity of polymers for any flexible chain architecture, including linear, ring, stars, to hyperbranched and dendrimers. This review then focuses on the static and dynamic properties of confined polymer chains. Depending on the value of channel size relative to the persistence length and effective width, the behaviors of a semiflexible polymer chain confined in a nanochannel can be categorized into four regimes as follows:de Gennes regime, extended de Gennes regime, Odijk regime and backfolded Odijk regime. In de Gennes regime, where the channel size is much bigger than the persistence length, the static and dynamic properties of confined semiflexible polymer chains can be explained by Blob theory and there is no essential difference between the flexible and semiflexible polymer chains. The semiflexible polymer chains in extended de Gennes regime can be described by replacing the spherical Blob in de Gennes regime with an anisomeric Blob. The confined extension and diffusion coefficient have the same scaling relationships with that in de Gennes regime. However, other properties including the confined free energy, variance of extension and effective spring constant exhibit different scalings. In Odijk regime, the confined chain is considered to be formed by repeating units of deflection segments and the chain is frequently deflected by channel walls; while in backfolded Odijk regime, the deflection segments can form hairpins inside the channel. Theoretically, new characteristic scales, such as the deflection length and global persistence length are introduced to clarify the differences between Odijk regime and backfolded Odijk regime. This review also summarizes two classic theories developed by de Gennes and Wu Chi for flow-induced polymer translocation. Based on the calculation of free energy, de Gennes pointed out that the critical flux of linear and branched polymer chains is independent of the channel size. Instead of calculating free energy, Wu Chi directly balanced confinement and hydrodynamic forces to obtain a unified scaling description of the critical flux for polymer chains with different topologies, and conducted that the critical flux decreases as the channel size increases. The difference between their theories is that they treated the confined blobs as non-draining and free-draining spheres, respectively. However, the confined blobs are partially permeable and the complicated hydrodynamic interactions indeed play an important role in polymer translocation, which worth further research. Finally, open issues and future prospects of confined polymer chains are discussed.