The notion that density structure reflects magnetic field lines makes it possible to deduce information on coronal magnetic fields from density measurements. The purpose of this paper is to summarize the observational evidence for ubiquitous open magnetic field lines in the inner corona from density measurements. Based on both global and filamentary structures, these density measurements explain the unexpected predominance of the radial component of coronal magnetic field discovered in polarimetric observations over three decades ago. © 2003 American Institute of Physics