The next generation of ground based telescopes, the so-called extremely large telescopes, will offer a significant leap in sensitivity and resolution compared to current telescopes. They also present a range of technical challenges. This thesis presents work on two important problems in implementing laser guide star adaptive optics on extremely large telescopes: focal anisoplanatism and turbulence profiling. The SPLASH (Sky-Projected Laser Array Shack-Hartmann) laser guide star wavefront sensing technique is described. The technique is shown to offer reduced focal anisoplanatism compared to a conventional laser guide star for large telescopes. The technique may also offer advantages for larger apertures, including extremely large telescopes, but simulations were limited to 8 metre apertures by currently available computing capabilities. A calibration method is presented for the SLODAR (Slope Detection and Ranging) turbulence profiling technique, along with an analysis of the effects of scintillation on SLODAR when the technique is applied on a small (~ 40 cm diameter)' telescope. A new variation on the SLODAR technique, SLOTDAR (Slope Detection and Ranging through a slot), is introduced, in which the spatial sampling can be optimised based on the brightness of the available reference stars.