Histone methyltransferase that specifically trimethylates 'Lys-9' of histone H3 using monomethylated H3 'Lys-9' as substrate. H3 'Lys-9' trimethylation represents a specific tag for epigenetic transcriptional repression by recruiting HP1 (CBX1, CBX3 and/or CBX5) proteins to methylated histones. Mainly functions in heterochromatin regions, thereby playing a central role in the establishment of constitutive heterochromatin at pericentric and telomere regions. H3 'Lys-9' trimethylation is also required to direct DNA methylation at pericentric repeats. SUV39H1 is targeted to histone H3 via its interaction with RB1 and is involved in many processes, such as repression of MYOD1-stimulated differentiation, regulation of the control switch for exiting the cell cycle and entering differentiation, repression by the PML-RARA fusion protein, BMP-induced repression, repression of switch recombination to IgA and regulation of telomere length. Component of the eNoSC (energy-dependent nucleolar silencing) complex, a complex that mediates silencing of rDNA in response to intracellular energy status and acts by recruiting histone-modifying enzymes. The eNoSC complex is able to sense the energy status of cell: upon glucose starvation, elevation of NAD(+)/NADP(+) ratio activates SIRT1, leading to histone H3 deacetylation followed by dimethylation of H3 at 'Lys-9' (H3K9me2) by SUV39H1 and the formation of silent chromatin in the rDNA locus. Recruited by the large PER complex to the E-box elements of the circadian target genes such as PER2 itself or PER1, contributes to the conversion of local chromatin to a heterochromatin-like repressive state through H3 'Lys-9' trimethylation (By similarity). L-lysyl(9)-[histone H3] + 3 S-adenosyl-L-methionine = 3 H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl(9)-[histone H3] + 3 S-adenosyl-L-homocysteine Negatively regulated by CCAR2. Interacts with H3 and H4 histones. Interacts with GFI1B, DNMT3B, CBX1, CBX4, CCAR2, MBD1, RUNX1, RUNX3, MYOD1, SMAD5 and RB1. Interacts with SBF1 through the SET domain. Interacts with HDAC1 and HDAC2 through the N-terminus and associates with the core histone deacetylase complex composed of HDAC1, HDAC2, RBBP4 and RBBP7. Component of the eNoSC complex, composed of SIRT1, SUV39H1 and RRP8 (By similarity). Interacts (via SET domain) with MECOM; enhances MECOM transcriptional repression activity. Interacts with LMNA; the interaction increases stability of SUV39H1. The large PER complex involved in the histone methylation is composed of at least PER2, CBX3, TRIM28, SUV39H1 and/or SUV39H2; CBX3 mediates the formation of the complex (By similarity). Associates with centromeric constitutive heterochromatin. Although the SET domain contains the active site of enzymatic activity, both pre-SET and post-SET domains are required for methyltransferase activity. The SET domain also participates in stable binding to heterochromatin (By similarity). In the pre-SET domain, Cys residues bind 3 zinc ions that are arranged in a triangular cluster; some of these Cys residues contribute to the binding of two zinc ions within the cluster. Phosphorylated on serine residues, and to a lesser degree, on threonine residues. The phosphorylated form is stabilized by SBF1 and is less active in its transcriptional repressor function (By similarity). Acetylated at Lys-266, leading to inhibition of enzyme activity. SIRT1-mediated deacetylation relieves this inhibition (By similarity). Belongs to the class V-like SAM-binding methyltransferase superfamily. Histone-lysine methyltransferase family. Suvar3-9 subfamily.