Protoplanetary discs consist of gas and dust - the remnants of the star formation process - found around stars in the first few million years of their life. Photoevaporation, whereby high-energy radiation from the central star heats disc material causing it to flow away in a wind, is one process thought to contribute to their ultimate dispersal. Previous studies have failed to reach a consensus on the main radiation which is responsible for this process, variably finding the X-ray, Extreme Ultraviolet, or Far Ultraviolet. These paradigms make very different predictions for the amount of mass lost to the winds, and consequently how important they are for disc evolution.

The primary aim of the thesis is to tackle this uncertainty from the following directions: a) by understanding the microphysical processes that underpin the differences in existing models in order to establish a comprehensive methodology for future state-of-the-art photoevaporation simulations that resolve the present disagreements; b) by considering how different wind models appear in observations of atomic forbidden emission lines and so how both line profiles and spatially resolved emission may be used to constrain the wind's nature; c) by including photoevaporation in models of disc evolution on secular timescales that predict its interplay with other processes - and how this manifests in disc demographic surveys - and thus determine how it contributes to the disc's ultimate dispersal.

I conclude that while EUV-driven models have underestimated the role of X-ray due to a lack of detail in the spectrum, the X-ray driven models have underestimated the cooling from molecular emission lines. Thus; the true picture may be expected to be somewhat intermediate between the two extremes. Constraints from disc demographics require low enough rates that discs survive to the age of older star forming regions even around low-mass stars, and there is time for dust to deplete considerably before the wind disperses the gas. Conversely, ratios of emission lines require a high enough mass-loss rate to ensure the wind is only weakly ionised.