The crystal structure of a material creates a periodic potential that electrons move through giving rise to its electronic band structure. When two-dimensional materials are stacked, the resulting moiré pattern introduces an additional periodicity so that the twist angle between the layers becomes an extra degree of freedom for the resulting heterostructure. As this angle changes, the electronic band structure is modified leading to the possibility of flat bands with localized states and enhanced electronic correlations1–6. In transition metal dichalcogenides, flat bands have been theoretically predicted to occur for long moiré wavelengths over a range of twist angles around 0° and 60° (ref. 4) giving much wider versatility than magic-angle twisted bilayer graphene. Here, we show the existence of a flat band in the electronic structure of 3° and 57.5° twisted bilayer WSe2 samples using scanning tunnelling spectroscopy. Our direct spatial mapping of wavefunctions at the flat-band energy show that the localization of the flat bands is different for 3° and 57.5°, in agreement with first-principles density functional theory calculations4.Using scanning tunnelling spectroscopy, the flat bands in twisted bilayer WSe2 are shown near both 0° and 60° twist angles.