What are the pathways involved in the repair of double-stranded DNA breaks?

Cells have two major pathways for repairing DSBs: nonhomologous end joining (NHEJ) and homologous recombination (HR). 

1. In homologous recombination, the process begins with the resection of the broken DNA ends, generating 3' single-stranded DNA (ssDNA) overhangs. The ssDNA then invades a homologous DNA sequence (typically the sister chromatid) forming a displacement loop. DNA synthesis occurs using the intact sister chromatid as a template, extending the invading strand and filling in the gap. Lastly, the DNA ends are ligated together, resulting in the accurate repair of the DSB. 
2. In NHEJ, the broken DNA ends are bound by DNA-dependent protein kinase (DNA-PK), which gathers other NHEJ factors to the site of the break. The processed DNA ends, prepared by nucleases and polymerases to remove damaged nucleotides, are then ligated together by DNA ligase IV.