Wave propagation in transmission lines has been the subject of study for many decades. In a transmission line, waves of different frequencies propagate with different velocities and different wavelengths. The relation between the phase advance of a wave and its frequency is given by the dispersion relation ω(β). A transmission line can have spatial or temporal periodicity. For a spatially periodic transmission line the dispersion relation displays phase advance periodicity and frequency gaps whilst for a temporally periodic transmission line the dispersion relation presents phase advance gaps and frequency periodicity. A dynamic medium is one in which at least one of the characteristics that define it changes with time. A dynamic medium with periodic permittivity ε(t) is periodic in ω and there are forbidden bands for the phase advance β. When a monochromatic plane wave of frequency ω is incident on such a medium, the reflected and transmitted waves contain harmonics of the modulation frequency Ω. Transmission lines are spatially periodic and are widely used to transport voltage signals. In this thesis, a transmission line with spatial and temporal periodicity and with a new modulation method is presented. The temporal periodicity is given by time-changing capacitors (varactors). A realistic model to describe this dynamic transmission line (DTL) is proposed. This model considers losses, voltage modulation effects and no linearity of varactors. A general solution for the dispersion relation is found and solved for different parameters of the DTL. An approximate solution that gives insight on DTLs performance is also found. It is proved that a DTL can be described as an effective medium for the long wavelength limit [C(t)/a = ε(t), L/a = μ, and βa << 1]. Experimental verification and comparison with theoretical results were made, the results include dispersion relations, harmonic generation and frequency beats.