It has been more than two decades since the copper-oxide high temperature superconductors were discovered. However, building a satisfactory theoretical framework to study these compounds still remains one of the major challenges in condensed matter physics. In addition to the mechanism of superconductivity, understanding the properties of the normal state is a major puzzle in itself. As these materials are doped Mott insulators, the interaction between electrons is particularly strong. The strong electron correlations are responsible for the breakdown of Fermi-liquid behavior in the normal state. A variety of experimental probes reveal anomalous features in these materials. Such anomalies are reflected in the photoemission spectra as well as transport coefficients such as resistivity, optical conductivity, Hall coefficient, thermoelectric power etc. The objective of this dissertation is to understand the anomalous features as universal features of doped Mott insulators arising entirely as a consequence of strong electron correlations, using the two-dimensional square lattice Hubbard model as the model Hamiltonian. This dissertation is organized into eight chapters. Chapter 1 is an introductory chapter that discusses some key issues. A brief introduction to the superconducting cuprates and their anomalous physical properties is given. Also included is an outline on Mott insulators and the concept of Mottness. Chapter 2 contains a discussion on Cluster Dynamical Mean Field Theory (CDMFT), the principal numerical technique to be implemented in this dissertation. Chapter 3 describes the exact low-energy theory of doped Mott insulators, which largely provides a theoretical framework to this dissertation. In Chapter 4, we compute the spectral function of the two-dimensional Hubbard model using CDMFT and study the origin of the kink feature observed in the electron dispersion measured by ARPES (Angle Resolved Photoemission Spectroscopy). In Chapter 5, the origin of the mid-IR band seen in optics experiments is studied. In Chapter 6, we study the universal sign change of the thermopower in the vicinity of optimal doping in the cuprates. Chapter 7 uses experimental data from Hall measurements to establish a connection between the pseudogap state and the charge-2e boson which emerges naturally in the exact low-energy theory of Mott systems. Chapter 8 is the concluding chapter which attempts to present all of our findings within the context of the central unifying theme of Mottness. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]