High-energy neutrinos could be produced in the interaction of charged cosmic rays with matter or radiation surrounding astrophysical sources. To look for transient sources associated with neutrino emission, a follow-up program of neutrino alerts has been operating within the ANTARES collaboration since 2009. This program, named TAToO, has triggered robotic optical telescopes (MASTER, TAROT, ROTSE and the SVOM ground based telescopes) immediately after the detection of any relevant neutrino candidate and scheduled several observations in the weeks following the detection. A subset of ANTARES events with highest probabilities of being of cosmic origin has also been followed by the Swift and the INTEGRAL satellites, the Murchison Widefield Array radio telescope and the H.E.S.S. high-energy gamma-ray telescope. The results of twelve years of observations are reported. In September 2015, ANTARES issued a neutrino alert and during the follow-up, a potential transient counterpart was identified by Swift and MASTER. A multi-wavelength follow-up campaign has allowed to identify the nature of this source and has proven its fortuitous association with the neutrino. No other optical and X-ray counterpart has been significantly associated with an ANTARES candidate neutrino signal. Constraints on transient neutrino emission have been set. The return of experience is particularly important for the design of the alert system of KM3NeT, the next generation neutrino telescope in the Mediterranean Sea.