The photolysis of methane is studied using photofragment imaging techniques. Our study reveals that the photolysis of methane proceeds via many different pathways. The photofragment imaging technique is used to resolve and characterize these various pathways and provides therefore unique insight into the dynamical processes that govern this photodissociation. The formation of H-atom photofragments following absorption of a Lyman-alpha photon, and H-2 photofragments following absorption of two ultraviolet photons (lambda=210-230 nm) are studied. The measured H-atom photofragment images reveal that a channel that produces fast H atoms concomitant with methyl fragments is dominant in the Lyman-alpha photolysis of methane. This channel leads to an anisotropic recoil of the fragments. A secondary channel is observed leading to the formation of somewhat slower H atoms, but an unique identification of this second channel is not possible from the data. At least part of these slower H atoms are formed via a channel that produces H atoms concomitant with CH and H-2 photofragments. The recoil of these slower H atoms appears to be isotropic. The measured, state-resolved H-2(v,J), photofragment images reveal that two channels lead to H-2 photofragments from the two-photon photolysis of methane : a channel that leads to H-2 products concomitant with methylene fragments; and a channel that leads to H-2 products concomitant with CH and H fragments. H-2(v,J) rotational and vibrational distributions are measured for each of these two channels separately, The H-2 products formed via the H-2+CH2 channel are rotationally and vibrationally highly excited, whereas those formed via the H-2+CH+H channel are rotationally and vibrationally cooler. Rotational distributions of H-2 formed via the H-2+CH+H channel are well reproduced by Boltzmann distributions. Results on D-2 elimination following two-photon photolysis. of CD4 are in general similar and in qualitative agreement with the results on CH4.