Compositions and methods are provided for modifying a genomic locus of interest in a eukaryotic cell, a mammalian cell, a human cell or a non-human mammalian cell using a large targeting vector (LTVEC) comprising various endogenous or exogenous nucleic acid sequences as described herein. Further methods combine the use of the LTVEC with a CRISPR/Cas system. Compositions and methods for generating a genetically modified non-human animal comprising one or more targeted genetic modifications in their germline are also provided.