Submitted on 13 Feb 2008 (v1), last revised 5 Mar 2008 (this version, v2).-- Some misprints and citations corrected.We find the most general supersymmetric solutions of ungauged N=1,d=4 supergravity coupled to an arbitrary number of vector and chiral supermultiplets, which turn out to be essentially pp-waves and strings. We also introduce magnetic 1-forms and their supersymmetry transformations and 2-forms associated to the isometries of the scalar manifold and their supersymmetry transformations. Only the latter can couple to BPS objects (strings), in agreement with our results.This work has been supported in part by the Spanish Ministry of Science and Education grants FPA2006-00783 and PR2007-0073, the Comunidad de Madrid grant HEPHACOS P-ESP-00346, the Spanish Consolider-Ingenio 2010 Program CPAN CSD2007-00042, and by the EU Research Training Network Constituents, Fundamental Forces and Symmetries of the Universe MRTN-CT-2004-005104.Peer reviewed