Proximity zones of quasars with redshifts z > 5.5 are unique probes of the growth of supermassive black holes, and a nuisance in the direct measurements of the mean free path of the photons that reionize the universe. Interestingly, such proximity zones have been at the centre of two observational puzzles in recent times: 1) about 10% of the measured proximity zone sizes in the quasar Lyman-alpha spectra seem to be too short to explain their black hole masses, and 2) when corrected for the proximity zones, the mean free path of ionizing photons at z ~ 6 appears to be much shorter than theoretical predictions. In this talk, I will present a model of quasar proximity zones that takes into account the patchiness of the ionization and thermal state of the IGM during reionization. I will show that the patchiness of reionization can relieve the tension between the proximity zone sizes and black hole masses to some degree, but not fully. Further, I will show how quasar proximity zones in an inhomogeneously ionized IGM affects mean free path measurements from rest-frame 912 A spectra at z ~ 6. By forward modelling the proximity zones, I will examine the consistency between the direct and indirect redshift-6 mean free path measurements. Finally, I will show that the observed distribution of proximity zone sizes can be explained by a model in which quasars are variable on timescales of ~10^6 yr and have short duty cycles. This conclusion, when combined with the measurements of black hole masses of these quasars, directly leads to a prediction of significant obscuration in high-redshift quasars. I will argue that measurements of this obscuration fraction using JWST can then place constraints on the seed mass and formation redshifts of black holes.