The two mechanisms employed by eukaryotes for repairing double strand breaks are: non-homologous end joining (NHEJ) and homology directed repair (HDR).
NHEJ inserts nucleotides at the site of the DSB, allowing the strand to re-join. This disrupts the coding region of the gene.
HDR uses homologous recombination to insert different length fragments into the DNA, joining the DSB back together. This mechanism can only be used when there is a homologous region of DNA present in the cell, restricting this repair mechanism to G2 and S phases of the cell cycle. Due to the use of a template, it is thought this repair mechanism is error-free.