Metallic nanocontacts consisting of just a single monatomic wire (atomic chain) connecting two macroscopic electrodes can be now fabricated, imaged, and explored by means of various techniques such as scanning tunneling microscopy or mechanically controllable break junctions. We present the first principles density functional theory study of such nanowire contacts making a special emphasis on the interplay between their magnetic and electron transport properties. We show the results for ferromagnetic Ni nanocontacts and for Pt nanocontacts where the one-dimensional monatomic wires (unlike to the bulk) were recently shown to develop magnetism.