The scope of the present doctoral thesis has been the conception of a novel and efficient method for decelerating, over a range of frequencies, and completely 'stopping' light (zero group velocity, vg = 0) inside solid-state materials, at room temperature. To this end, we analytically show that an adiabatically tapered waveguide having a core of a lossless negative refractive index (NRI) metamaterial (MM) and claddings made of normal dielectrics can 'trap' a light pulse in such a way that each individual frequency component of the pulse is stopped at a different point along the waveguide, forming what we have called a 'trapped rainbow'. Crucially, it is shown that light can efficiently be in-coupled inside such a waveguide heterostructure from a normal dielectric waveguide, since with a suitable design one can achieve simultaneous thickness-, mode- and characteristic-impedance-matching between the two waveguides. A pertinent analysis reveals that the optical path length of a 'trapped' light ray (associated with a particular frequency component of the pulse), as well as the corresponding effective thickness of the NRI waveguide itself, become exactly zero. The ray circulates at the point where it is trapped in such a way that its trajectory forms what we have called (in view of its characteristic hourglass form) an 'optical clepsydra'. Furthermore, we introduce a novel methodology that allows for obtaining ultra- low- or zero-loss magnetic metamaterials over a continuous range of frequencies. We analytically prove that a higher-degrees-of-freedom MM design methodology based on equivalent electrical circuits with more than one mesh leads to metamaterial magnetism with either ultra-high figures-of-merit or with perfectly lossless performance over a broad range of frequencies. The so-obtained lossless metamaterial magnetism has a truly intrinsic character, and as such is scalable and can be implemented at any frequency regime, from the radio up to the optical domain.