The eleventh generation of the International Geomagnetic Reference Field (IGRF) was agreed in December 2009 by a task force appointed by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD. New spherical harmonic main field models for epochs 2005.0 (DGRF-2005) and 2010.0 (IGRF-2010), and predictive linear secular variation for the interval 2010.0-2015.0 (SV-2010-2015) were derived from weighted averages of candidate models submitted by teams led by DTU Space, Denmark (team A); NOAA/NGDC, U.S.A. (team B); BGS, U.K. (team C); IZMIRAN, Russia (team D); EOST, France (team E); IPGP, France (team F); GFZ, Germany (team G) and NASA-GSFC, U.S.A. (team H). Here, we report the evaluations of candidate models carried out by the IGRF-11 task force during October/November 2009 and describe the weightings used to derive the new IGRF-11 model. The evaluations include calculations of root mean square vector field differences between the candidates, comparisons of the power spectra, and degree correlations between the candidates and a mean model. Coefficient by coefficient analysis including determination of weighting factors used in a robust estimation of mean coefficients is also reported. Maps of differences in the vertical field intensity at Earth's surface between the candidates and weighted mean models are presented. Candidates with anomalous aspects are identified and efforts made to pinpoint both troublesome coefficients and geographical regions where large variations between candidates originate. A retrospective analysis of IGRF-10 main field candidates for epoch 2005.0 and predictive secular variation candidates for 2005.0-2010.0 using the new IGRF-11 models as a reference is also reported. The high quality and consistency of main field models derived using vector satellite data is demonstrated; based on internal consistency DGRF-2005 has a formal root mean square vector field error over Earth's surface of 1.0 nT. Difficulties nevertheless remain in accurately forecasting field evolution only five years into the future.