Vector is a nucleic acid molecule that can replicate in a host cell and integrate foreign DNA. It must have an origin of replication and be small in size. Good vectors have selectable marker genes, sites for restriction enzymes, and for expression vectors, control elements like promoters. Common vectors include plasmids, bacteriophages, cosmids, and artificial vectors like pBR322 and pUC, which were derived from plasmids for cloning and expression purposes.