This paper uses tools in quasi-homogeneous normal form theory to discuss certain aspects of reversible vector fields around an equilibrium point. Our main result provides an algorithm, via Lie Triangle, that detects the non-reversibility of vector fields. That is, it is possible to decide whether a planar center is not reversible. Some of the theory developed is also applied to get further results on nilpotent and degenerate polynomial vector fields. We find several families of nilpotent centers which are non-reversible. (C) 2010 Elsevier Ltd. All rights reserved.732510525Ministerio de Educacion y CienciaFEDER [MTM2007-64193]Consejeria de Educacion y Ciencia de la Junta de Andalucia [P08-FQM-03770, FQM-276]FEDER [MTM2007-64193]Consejeria de Educacion y Ciencia de la Junta de Andalucia [P08-FQM-03770, FQM-276]