The château rises on a rocky spur immediately above the old town, a massive late-medieval pile of grey stone with a tall square keep (the Tour de la Reine, twelfth century) and several later wings. It was the seat of the Counts of Geneva from the eleventh century, then of the cadet Dukes of Genevois-Nemours from the sixteenth, before falling into ruin in the eighteenth and being saved by the city in 1953.
The interior is now the Musée-Château d'Annecy, a mixed museum of regional art, Alpine ethnography, archaeology, and a strong contemporary section in the Logis Nemours. The medieval prisons in the basement and the courtyard with views over the rooftops are highlights even if the collections don't grab you. Allow 90 minutes; combined ticket with the Palais de l'Île saves money.