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© ESO 2011. Supported by INFN Padova.We would like to thank the Instituto de Astrofisica de Canarias for the excellent working conditions at the Observatorio del Roque de los Muchachos in La Palma. The support of the German BMBF and MPG, the Italian INFN, the Swiss National Fund SNF, and the Spanish MICINN is gratefully acknowledged. This work was also supported by the Marie Curie program, by the CPAN CSD2007-00042 and MultiDark CSD2009-00064 projects of the Spanish Consolider-Ingenio 2010 programme, by grant DO02-353 of the Bulgarian NSF, by grant 127740 of the Academy of Finland, by the YIP of the Helmholtz Gemeinschaft, by the DFG Cluster of Excellence "Origin and Structure of the Universe", and by the Polish MNiSzW Grant N N203 390834. Authors wish to thank Alan Marscher for useful discussions and the referee Elena Pian for useful comments on the earlier version of the paper., Context. 3C 279, the first quasar discovered to emit VHE gamma-rays by the MAGIC telescope in 2006, was reobserved by MAGIC in January 2007 during a major optical flare and from December 2008 to April 2009 following an alert from the Fermi space telescope on an exceptionally high gamma-ray state. Aims. The January 2007 observations resulted in a detection on January 16 with significance 5.4 sigma, corresponding to a F (>150 GeV) (3.8 +/- 0.8) x 10(-11) ph cm(-2) s(-1) while the overall data sample does not show significant signal. The December 2008-April 2009 observations did not detect the source. We study the multiwavelength behaviour of the source at the epochs of MAGIC observations, collecting quasi-simultaneous data at optical and X-ray frequencies and for 2009 also gamma-ray data from Fermi. Methods. We study the light curves and spectral energy distribution of the source. The spectral energy distributions of three observing epochs (including the February 2006, which has been previously published) are modelled with one-zone inverse Compton models and the emission on January 16, 2007 also with two zone model and with a lepto-hadronic model. Results. We find that the VHE gamma-ray emission detected in 2006 and 2007 challenges standard one-zone model, based on relativistic electrons in a jet scattering broad line region photons, while the other studied models fit the observed spectral energy distribution more satisfactorily., INFN Padova, German BMBF, German MPG, Italian INFN, Swiss National Fund SNF, Spanish MICINN, Marie Curie program, CPAN, Spanish Consolider-Ingenio, Bulgarian NSF, Academy of Finland, YIP of the Helmholtz Gemeinschaft, DFG, Depto. de Estructura de la Materia, Física Térmica y Electrónica, Fac. de Ciencias Físicas, TRUE, pub