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Presented at the XXXIV Mazurian Lakes Conference on Physics, Piaski, Poland, September 6–13, 2015.In this contribution, we review some recent theoretical advances for the calculation of breakup cross sections in reactions induced by weakly-bound nuclei.This work has been partially supported by the Spanish Ministerio de Economía y Competitividad, under grant FIS2013-41994-P, by the Spanish Consolider-Ingenio 2010 Programme CPAN (CSD2007-00042) and by Junta\udde Andalucía (FQM160, P07-FQM-02894), and by the European Commission, Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 600376. J.A.L. is funded by a Marie Curie Piscopia fellowship at the University of Padova. J.L. is partially supported by a grant funded by the China Scholarship Council. M.G.-R. acknowledges a research grant by the Ministerio de Educación, Cultura y Deporte of Spain. R.D. acknowledges support by the Fundacão para a Ciência e a Tecnologia (FCT) Grant No. SFRH/BPD/78606/2011.Peer Reviewe

Recent Developments for the Calculation of Elastic and Non-elastic Breakup of Weakly-bound Nuclei