Main approaches and methods used for constructing "jamping" and cDNA libraries, including novel ones, that omit the employment of methylases and linkers, are presented. The advantages and drawbacks of the well-known and new lambda vectors, suitable for the purposes mentioned, are discussed. Special attention is paid to diphasmids lambda ZAP, lambda SK12, lambda SK15, that combine features of lambda and M13 phages and of plasmids. The convenience and difficulties of "jumping" libraries for physical mapping of chromosomes are briefly considered.