We will discuss how topological field theories have been used in order to effectively describe the properties of the topological materials[1,2]. We mainly concentrate on topological insulators giving an account of the recent experimental advancements[3]. We briefly summarize the research done on the BF theory and its restriction at the boundary to identify the nature of the gapless fermionic modes localized at the surface[4].Finally we will show how transport properties of the edge states may be used to detect the existence of fractional topological insulators[5]. [1] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010) [2] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011) [3] B. A. Bernevig, T. L. Hughes, S.-C. Zhang, Science 314,1757 (2006); M. Ko ̈nig, S. Weidmann, C. Bru ̈ne, A. Roth, H. Buhmann, L. W. Molenkampf, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007); A. Roth, C. Bru ̈ne, H. Buhmann, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Science 325, 294 (2009) [4] A. Blasi, A. Braggio, M. Carrega, D. Ferraro, N. Maggiore, N. Magnoli New J. Phys. 14, 013060 (2012); A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli Adv. High En. Phys. 2014, 635286; A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli JHEP 1404 (2014) 142; A. Amoretti, A. Braggio, G. Caruso, N. Maggiore, N. Magnoli Phys. Rev. D 90, 125006 (2014) [5] G. Dolcetto, L. Vannucci, A. Braggio, R. Raimondi, M. Sassetti Phys. Rev. B 90, 165401 (2014).