Beauxbatons: Beauxbatons is a wizarding school located somewhere in France. During the time of the Triwizard Tournament, the headmistress was Olympe Maxime. Students who attend Beauxbatons wear pale blue robes. Fleur Delacour was selected as Triwizard Champion from Beauxbatons, and she spent most of her time at Hogwarts complaining about various things. According to Fleur, Beauxbatons students take their exams in their 6th year, as opposed to Hogwarts students who take them in their 5th and 7th years. The glittering palace of Beauxbatons is also unplottable, which protects it from rival schools. Beauxbatons translates roughly to "beautiful wands" in French.
Durmstrang: Durmstrang Institute is an infamous wizarding school located somewhere in northern Europe. It has a bad reputation for actually teaching its students the Dark Arts, instead of just how to defend yourself against them. During the time of the Triwizard Tournament, the headmaster of Durmstrang was Igor Karkaroff (a former Death Eater). After Voldemort's re-birth, Karkaroff did not return to him, and for this he paid a price. In The Half-Blood Prince Remus Lupin announces that Karkaroff was found dead, murdered by the Death Eaters. We do not know who replaced him as headmaster. The students at Durmstrang wear dark red robes and heavy fur coats. This is because is because the school is located somewhere extremely cold. The Triwizard Champion for Durmstrang turned out to be Viktor Krum, seeker of the Bulgarian Quidditch team. Unlike Fleur Delacour, Viktor seemed to enjoy his time at Hogwarts and preferred it to his own school. Durmstrang Institute is a castle that reaches four stories high, and although they have wonderful grounds, it is always much too cold to go outside.