Materials with resonant features can have a rapidly changing refractive index spectrally or temporally that gives rise to a changing group index. Depending on the wavelength of the input light, this light can see regimes of normal or anomalous dispersion. Within these regions, the group index can become large, depending on the optical effect used, and give rise to slow or fast light effects. This thesis covers two platforms that exhibit the use of slow and fast light. Slow and fast light are used to manipulate and enhance other optical effects in question. As the focus of this thesis, we examine a rotating ruby rod and spaceplates based on multilayer stacks, both considered as slow- and fast-light media. Light propagation through each platform is modelled and simulated to compare to the experiment. The simulation results for both platforms match well with the measured experimental effects and show the feasibility and utility of slow or fast light to manipulate or enhance optical effects. We simulate light propagation in a rotating ruby rod as a rotating, anisotropic medium with thermal nonlinearity using generalized nonlinear Schrodinger equations, modelling the interplay of many optical effects, including nonlinear refraction, birefringence, and a nonlinear group index. The results are fit to experimentally measured results, revealing two key relationships: The photon drag effect can have a nonlinear component that is dependent on the motion of the medium, and the temporal dynamics of the moving birefringent nonlinear medium create distorted figure-eight-like transverse trajectories at the output. We observe light propagation through a rotating ruby rod where the light is subject to drag. Light drag is often negligible due to the linear refractive index but can be enhanced by slow or fast light, i.e., a large group index. We find that the nonlinear refractive index can also play a crucial role in the propagation of light in moving media and results in a beam deflection. An experiment is performed on the crystal that exhibits a very large negative group index and a positive nonlinear refractive index. The negative group index drags the light opposite to the motion of the medium. However, the positive nonlinear refractive index deflects the beam along with the motion of the medium and hinders the observation of the negative drag effect. Therefore, it is deemed necessary to measure not only the transverse shift of the beam but also its output angle to discriminate the light-drag effect from beam deflection. This work could be applied to dynamic control of light trajectories, for example, beam steering and velocimetry. For the following two chapters, we will focus on a different slow-light platform. This platform focuses on optics that we developed and tested that compress the amount of free-space propagation using multilayered stacks of thin films known as spaceplates. We design and characterize four multilayer stack-based spaceplates based on two design philosophies: coupled resonators and gradient descent. Using the transfer-matrix method, we simulate and extract the angular and wavelength dependence of the transmission phase and transmittance to extract and predict compression factors for each device. A brief theoretical investigation is developed to predict resonance positions, spacing, and bandwidth. We measure the transverse walk-off to extract the compression factor of four multilayer stack-based spaceplates as a function of angle and wavelength. One of the devices was found to have a compression factor of $R=176\pm14$, more than ten times larger than previous experimental records. We increased the numerical aperture of one of the devices by ten times, and we still observed a compression factor of $R=30\pm3$, two times larger than the most recent experimental measurements. We also measured focal shifts up to 800 microns, more than 40 times the device size, typically 10-12 microns thick. The multilayer stack-based spaceplates we studied here show great promise for ultrathin flat optical systems that can easily be integrated into a modern-day imaging system.