Structure-specific endonucleases mediate cleavage of DNA structures formed during repair of collapsed replication forks and double-strand breaks (DSBs). Here, we identify BTBD12 as the human ortholog of the budding yeast DNA repair factor Slx4p and D. melanogaster MUS312. Human SLX4 forms a multiprotein complex with the ERCC4(XPF)-ERCC1, MUS81-EME1, and SLX1 endonucleases and also associates with MSH2/MSH3 mismatch repair complex, telomere binding complex TERF2(TRF2)-TERF2IP(RAP1), the protein kinase PLK1 and the uncharacterized protein C20orf94. Depletion of SLX4 causes sensitivity to mitomycin C and camptothecin and reduces the efficiency of DSB repair in vivo. SLX4 complexes cleave 3' flap, 5' flap, and replication fork structures; yet unlike other endonucleases associated with SLX4, the SLX1-SLX4 module promotes symmetrical cleavage of static and migrating Holliday junctions (HJs), identifying SLX1-SLX4 as a HJ resolvase. Thus, SLX4 assembles a modular toolkit for repair of specific types of DNA lesions and is critical for cellular responses to replication fork failure.