The schools of Shammai and Hillel for the very first time disagreed regarding a case of Jewish law. This occurred around the turn of the 1st century. In the ensuing generations, the schools argued regarding many different laws, until the law was established according to the teachings of the "House of Hillel" -- with the exception of a few instances. According to tradition, following the arrival of the Moshiach the law will follow the rulings of the House of Shammai.
All throughout, the members of the two schools maintained friendly relations with each other.