Left handed materials (LHMs) are artificial materials that have negative electrical permittivity, negative magnetic permeability, and negative index of refraction across a common frequency band. They possess electromagnetic (EM) properties not found in nature. LHMs have attracted tremendous attention because of their potential applications to build the perfect lens and cloaking devices. In the past few years there has been ample proof for the existence of LHMs in the microwave frequency range. Recently, researchers are trying hard to push the operating frequency of LHMs into terahertz and the optical regime.;In this thesis, we start with the theoretical prediction of left handed materials made by Veselago 40 years ago, introducing the unique electromagnetic properties of the left handed materials. After discussing the realization of LHMs by the split ring resonators (SRRs) and wire designs, we briefly review the development of LHMs from microwave frequency to the optical regime. We discuss the chiral metamaterial, which provides an alternative approach to realize negative refractive index.;In Chapter 2, we discuss the electromagnetic properties of the SRRs and the breakdown of linear scaling properties of SRRs at infrared and optical frequencies. By discussing the current modes, and the electric and magnetic moments, we study three resonance modes of SRR with respect to different polarizations of EM waves. Through numerical simulations, we find the breakdown of linear scaling, due to the free electron kinetic energy for frequencies above 100 THz. This result is important. It proves that researchers cannot push metamaterials into the optical regime by just scaling down the geometrical size of metamaterial designs used at low frequency.;Due to the breakdown of the linear scaling property, a much smaller structure size of LHMs design is required in the optical regime, so new designs with simpler topology are needed.;In Chapter 3, we discuss a short wire pair design, which has a distinct advantage over conventional SRRs. We systemically study the electromagnetic properties of the short wire pair design. We determine the criteria overlaps the electric and magnetic resonances of short wire pairs. Using an H-shaped short wire pairs design, we demonstrate negative refractive index experimentally.;In Chapter 4, we introduce a LHM design using short wire pairs with long wires, which avoid the difficulty of overlapping the electric and magnetic resonances. We also discussed the relationship between three important LHM designs suitable for the optical regime: double gap SRRs, the short wire pairs, and the fishnet structure.;Compared to LHMs at microwave frequencies, the current designs at optical frequencies suffer from high losses which limit their potential applications in the area requiring low losses, such as the perfect lens. In Chapter 5, we investigate the role of losses of the short wire pairs and the fishnet structures. We find the losses can be reduced substantially by increasing the effective inductance to capacitance ratio, L/C, especially at THz frequencies and in the optical regime.