This thesis investigates whether laser-driven plasma can be used as an analogue model of gravity in order to investigate Hawking radiation. An action describing laser-driven plasma is derived, and effective metrics are obtained in various regimes from the resulting field equations. Effective metrics exhibiting different behaviour are analysed by considering different forms of the fields. One of the effective metrics has the required properties for the analysis of Hawking radiation. It is shown that for a near-IR laser the Hawking temperature is about 4.5 K, which is small compared to typical plasma temperatures. However the waist of the laser is shown to have significant impact on the resulting Hawking temperature. As such it may be possible to obtain Hawking temperatures of several hundred Kelvin with a pulse width of a few $\mu$m. A new approach to investigating quantum fluctuations in an underdense laser-driven plasma is also presented that naturally emerges from the model underpinning the above studies. It is shown that the 1-loop effective action is expressible in terms of a massless field theory on a dilatonic curved background. Plane wave perturbations to the field equations are analysed for fields which are linear in Minkowski coordinates, and two dispersion relations are obtained. The impact on a Gaussian wave packet is calculated, suggesting it may be possible to experimentally verify this theory by utilising an x-ray laser.