The structural, electronic, optical, and photocatalytic properties of out-of-plane and in-plane heterostructures of transition metal dichalcogenides are investigated by (hybrid) first principles calculations. The out-of-plane heterostructures are found to be indirect band gap semiconductors with type-II band alignment. Direct band gaps can be achieved by moderate tensile strain in specific cases. The excitonic peaks show blueshifts as compared to the parent monolayer systems, whereas redshifts occur when the chalcogen atoms are exchanged along the series S-Se-Te. Strong absorption from infrared to visible light as well as excellent photocatalytic properties can be achieved.