The main objective of the ALICE experiment is to study the properties and the evolution of the high-energy density system created in relativistic heavy-ion collisions at the LHC. For that purpose, ALICE has unique particle identification capabilities that enable the detection of weakly-decaying particles in the high-multiplicity environment created in lead-lead (Pb-Pb) collisions. In this work, we discuss the systematic measurements of strange and multi-strange hadrons performed by ALICE for proton-proton (pp), proton-lead (p-Pb) and Pb-Pb collisions. Production rates measured for p-Pb and Pb-Pb are compared to predictions from statistical hadronization models and to measurements performed in pp collisions. These data are also used for a brief discussion on strangeness enhancement.5561 Carminati, F., (2004) J. Physics G: Nucl. Particle Phys., 30, p. 1517. , ALICE CollaborationAbelev, B., (2013) Phys. Rev. Lett., 111 (22), p. 222301. , ALICE CollaborationAbelev, B., (2014) Phys. Lett. B, 728, pp. 216-227. , ALICE CollaborationBrun R et al 1985 CERN Data Handling Division DD/EE/841Brun R et al 1994 CERN Program Library LongWrite- up, W5013Andronic, A., Braun-Munzinger, P., Stachel, J., (2009) Phys. Lett. B, 673 (2), pp. 142-145Braun-Munzinger P, Redlich K and Stachel J 2003 arXiv:nucl-th/0304013Wheaton, S., Cleymans, J., Hauer, M., (2009) Comput. Phys. Commun., 180 (1), pp. 84-106Petran, M., Letessier, J., Petracek, V., Rafelski, J., (2013) Phys. Rev. C, 88 (3), p. 034907Bellwied, R., Borsanyi, S., Fodor, Z., Katz, S., Ratti, C., (2013) Phys. Rev. Lett., 111 (20), p. 202302Rafelski, J., Müller, B., (1982) Phys. Rev. Lett., 48 (16), pp. 1066-1069Abelev, B., (2009) Phys. Rev. C, 79 (3), p. 034909. , STAR CollaborationAntinori, F., (2006) J. Phys. G: Nucl. Phys., 32 (4), p. 427. , NA57 CollaborationAntinori, F., (2010) J. Phys. G: Nucl. Phys., 37 (4), p. 045105. , NA57 CollaborationAamodt, K., (2011) Phys. Rev. Lett., 106 (3), p. 032301. , ALICE Collaboration