Several analytical mean field models are presented for the class of stimuli responsive polymers that are driven by the lower critical solution temperature (LCST) transition. For solutions above the polymer crossover concentration, a hybrid model combines lattice-fluid excluded volume and van-der-Waals interactions with a combinatorial approach for the statistics of hydrogen bonding, hydration, and ionic bonding. This approach yields models for the LCST of both neutral polymers and lightly charged polyelectrolytes in aqueous salt solution. The results are shown to be in semi-quantitative agreement with experimental data for the cloud point of polyethylene oxide (PEO) in aqueous solution with various salts, and some aspects of the lyotropic series are reproduced. Results for lightly charged polyelectrolytes are compared to and shown to be in qualitative agreement with aspects of experimentally observed behavior. Finally, a framework is established for extension of these models to further aspects of the lyotropic series and polyelectrolyte behavior. At the nanoscale, lattice fluid (LF) and scaled particle theory (SPT) approaches are employed to model the LCST-related coil-globule-transition (CGT) of isolated polymer chains in highly dilute solution. The predicted CGT behavior semi-quantitatively correlates with experimental results for several polymer-solvent systems and over a range of pressures. Both the LF and SPT models exhibit a heating induced coil-to-globule transition (HCGT) temperature that increases with pressure until it merges with a cooling induced coil-to-globule transition (CCGT). The point at which the CCGT and HCGT meet is a hypercritical point that also corresponds to a merging of the lower critical and upper critical solution temperatures. Theoretical results are discussed in terms of a generalized polymer/solvent phase diagram that possesses three hypercritical points. Within the lattice model, a dimensionless transition temperature [author gives mathematical symbol] is given for a long chain simply by the equation [author gives mathematical equation], where [part of the equation] is the bulk solvent occupied volume fraction at the transition temperature. Furthermore, there is a critical value of the ratio of polymer to solvent S-L characteristic temperature below which no HCGT transition is predicted for an infinite chain. / text