The current museum of Cuenca has its origin in the one that D. Francisco Suay, mayor and teacher of Valeria, created in that town, collecting Roman objects from the Roman city and from other origins and chronology. In 1963 all the administrations agreed to locate the Provincial Archaeological Museum in Cuenca, in the old Pósito del Almudí, where the materials of Valeria, the donated funds and the pieces of the archaeological excavations that were developed in the province were transferred. Some pieces were also recovered from the disentailments and collected in the 19th century, in a museum that disappeared in the 1930s.
In 1973 the Museum was integrated in the National Patronage of Museums, of the Ministry of Education and Culture, in 1974 it was opened to the public in the building of its present location in Obispo Valero street and in 1984 its management was transferred to the Junta de Comunidades de Castilla-la Mancha. Between 1981 and 1982 its exterior image was modified following the project of the painter Miguel Zapata and its interior was remodeled, in 1990 the rooms dedicated to Prehistory and Protohistory were updated and since 2014 new pieces have been added to the exhibition and some contents have been updated.
The museum is located in the historic center of Cuenca in the so-called "Casa del Curato", since in the 19th century and until 1930 it was the Rectory House of the parishes of San Martín and Santiago. It is a 14th century building that preserves remains of its primitive Gothic construction and a 15th century coffered ceiling decorated with the arms of the Luna and Albornoz families. In the 16th century it was the seat of the Court of the Inquisition of Cuenca. For years the rehabilitation of the adjacent buildings has been pending to increase the exhibition space. The collections of the Museum of Cuenca are grouped in three sections, Archaeology, Fine Arts and Oenology, but in its three floors of permanent exhibition, due to the lack of space, only archaeological pieces and some of Fine Arts are exhibited. The exhibition covers the history of the province of Cuenca from the Paleolithic to the 20th century:
In the prehistoric and protohistoric stages, we can mention the Paleolithic of Valmayor, Carrascosa or El Provencio, the Neolithic of Verdelpino, several idols and stelae of the Chalcolithic and Bronze Age, such as the Chillarón and Hinojosa, the sword of Carboneras, the bell-shaped ceramics of Alto del Romo and those of the Dornajos type from the site of the same name, the Iron I ceramics from the necropolis of Carrascosa del Campo and Pajaroncillo, and the settlements of Reillo or Enguidanos, the Iron II materials of Celtic and Iberian type from the necropolis of Villar and silver treasures such as those of Valeria and Salvacañete.