Flow friction reduction by polymers is widely applied in the oil and gas industry for flow enhancement or to save pumping energy. The huge benefit of this technology has attracted many researchers to investigate the phenomenon for 70 years, but its mechanism is still not clear. The objective of this thesis is to investigate flow drag reduction with polymer additives, develop predictive models for flow drag reduction and its degradation, and provide new insights into the drag reduction and degradation mechanism. The thesis starts with a semi-analytical solution for the drag reduction with polymer additives in a turbulent pipe flow. Based on the FENE-P model, the solution assumes complete laminarization and predicts the upper limitation of drag reduction in pipe flows. A new predictive model for this upper limit is developed considering viscosity ratios and the Weissenberg number - a dimensionless number related to the relaxation time of polymers. Next, a flow loop is designed and built for the experimental study of pipe flow drag reduction by polymers. Using a linear flexible polymer - polyethylene oxide (PEO) - in water, a series of turbulent flow experiments are conducted. Based on Zimm's theory and the experimental data, a correlation is developed for the drag reduction prediction from the Weissenberg number and polymer concentration in the flow. This correlation is thoroughly validated with data from the experiments and previous studies as well. To investigate the degradation of drag reduction with polymer additives, a rotational turbulent flow is first studied with a double-gap rheometer. Based on Brostow's assumption, i.e., the degradation rate of drag reduction is the same as that of the molecular weight decrease, a correlation of the degradation of drag reduction is established, along with the proposal of a new theory that the degradation is a first-order chemical reaction based on the polymer chain scission. Then, the accuracy of the Brostow's assumption is examined, and extensive experimental data indicate that it is not correct in many cases. The degradation of drag reduction with polymer additives is further analyzed from a molecular perspective. It is found that the issue with Brostow's theory is mainly because it does not consider the existence of polymer aggregates in the flow. Experimental results show that the molecular weight of the degraded polymer in the dilute solution becomes lower and the molecular weight distribution becomes narrower. An improved mechanism of drag reduction degradation considering polymer aggregate is proposed - the turbulent flow causes the chain scission of the aggregate and the degraded aggregate loses its drag-reducing ability. Finally, the mechanism of drag reduction and degradation is examined from the chemical thermodynamics and kinetics. The drag reduction phenomenon by linear flexible polymers is explained as a non-spontaneous irreversible flow-induced conformational-phase-change process that incorporates both free polymers and aggregates. The entire non-equilibrium process is due to the chain scission of polymers. This theory is shown to agree with drag reduction experimental results from a macroscopic view and polymer behaviours from microscopic views. The experimental data, predictive models, and theories developed in this thesis provide useful new insights into the design of flow drag reduction techniques and further research on this important physical phenomenon.