Oxygenase that can act as both a histone lysine demethylase and a ribosomal histidine hydroxylase. Specifically demethylates 'Lys-4' (H3K4me) and 'Lys-36' (H3K36me) of histone H3, thereby playing a central role in histone code. Preferentially demethylates trimethylated H3 'Lys-4' (H3K4me3) and monomethylated H3 'Lys-4' (H3K4me1) residues, while it has weaker activity for dimethylated H3 'Lys-36' (H3K36me2). Also catalyzes the hydroxylation of 60S ribosomal protein L8 on 'His-216'. Acts as a regulator of osteoblast differentiation via its interaction with SP7/OSX by demethylating H3K4me and H3K36me, thereby inhibiting SP7/OSX-mediated promoter activation. May also play a role in ribosome biogenesis and in the replication or remodeling of certain heterochromatic region. Participates in MYC-induced transcriptional activation (By similarity). 2-oxoglutarate + L-histidyl-[protein] + O2 = (3S)-3-hydroxy-L-histidyl-[protein] + CO2 + succinate 2 2-oxoglutarate + N(6),N(6)-dimethyl-L-lysyl(36)-[histone H3] + 2 O2 = 2 CO2 + 2 formaldehyde + L-lysyl(36)-[histone H3] + 2 succinate Binds 1 Fe(2+) ion per subunit. Interacts with SP7/OSX; the interaction is direct (By similarity). Interacts with MYC. Interacts with PHF19; leading to its recruitment to H3K36me3 sites (By similarity). Belongs to the ROX family. NO66 subfamily.