This paper describes the algorithms used by the CMS experiment to reconstruct and identify tau to hadrons + tau neutrino decays during Run 1 of the LHC. The performance of the algorithms is studied in proton-proton collisions recorded at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.7 inverse femtobarns. The algorithms achieve an identification efficiency of 50-60%, with misidentification rates for quark and gluon jets, electrons, and muons between per mille and per cent levels.