In this thesis I have studied how discs around young stars evolve and disperse. In particular, I build models which combine viscous evolution with photoevaporation, as previous work suggests that photoevaporation can reproduce the observed disc evolution and dispersal time-scales. The main question this thesis attempts to address is: Can photoevaporation provide a dominant dispersal mechanism for the observed population of young stars?

Photoevaporation arises from the heating that high energy (UV and X-ray) photons provide to the surface layers of a disc. Before I started this work, only photoevaporation from a pure EUV radiation field was described within a hydrodynamic framework. Therefore, I start by building a hydrodynamic solution to the pure X-ray photoevaporation problem, and then extend this solution to the entire high energy spectrum. This hydrodynamic model leads me to conclude that it is the X-ray radiation field that sets the mass-loss rates. These mass-loss rates scale linearly with X-ray luminosity, are independent of the underlying disc structure and explicitly independent of stellar mass. I build a radiation-hydrodynamic algorithm, based on previous work, to describe the process of X-ray heating in discs. I then use this algorithm to span the full range of observed parameter space, to fully solve the X-ray photoevaporation problem. I further extend the algorithm to roughly approximate the heating an FUV radiation field would have on the photoevaporative flow, as well as separately testing the effect an EUV radiation field will have. These numerical tests are in agreement with the hydrodynamic model derived. Specifically, it is the X-rays that are driving the photoevaporative flow from the inner disc.

Armed with an accurate description of the photoevaporative mass-loss rates from young stars, I consider the evolution of a population of disc-bearing, young ($0.7$\msun) stars, in order to asses photoevaporation's role as a dispersal mechanism. This study shows that the observed spread in X-ray luminosity of young stars is sufficient to drive the dispersal of the entire population of discs, reproducing both the required time-scales and the required spread in observables (disc lifetime, accretion rate). I also show that a large fraction of the observed population of `transition' discs are consistent with being created through photoevaporation.

Having shown photoevaporation can provide a dominant dispersal mechanism for a population of discs, I attempt to describe some direct observable consequences of photoevaporation, both through gas tracers and dust emission. During this work, the first direct evidence of a photoevaporative flow emerging from a young star was obtained from TW Hya, in the NeII 12.8$\mu$m line. Therefore, I discuss this result within the framework of the X-ray photoevaporation model. Furthermore, I suggest that emission from the photoevaporative flow is the origin of the unexplained, blue-shifted, OI 6300\AA~ line observed around all young stars that possess discs. I then described the properties of the dust particles that may be entrained within the photoevaporative flow. The total dust mass in the flow is found to be small compared to the disc, although such a region becomes observable once the disc presents as edge-on, obscuring the central star and hot inner disc. I discuss the emission from these regions and compare them to the sample of currently imaged edge-on discs.

The presented photoevaporation model reproduces all of the current observations, and I discuss some predictions it makes with regard to future observations. Finally, photoevporation may have some intriguing consequences on planet formation and dust evolution that warrant further investigation.