The ‘Posito (old granary) building is a was constructed in the sixteenth century as indicated by the date engraved on the facade. It was connected to the  Alhóndiga through a vault being the important store house of the grain.  

In 1502 King Charles I was made aware of the need to build a new prison in Baeza due to the poor conditions of the existing one. The building was constructed in 1520 and the Casa de Corregidor was constructed in 1559.

The Casa del Populo was built around 1535 in a Renaissance architectural style in two sections. In the lower section there are six linteled openings, one for each Notary's Office. On the façade between each office there are ornamental columns ‘supporting’ a lateral lintel and above this, keystones decorated with engravings of seven lions. In between on the façade are six shields of the city.

The old butchers building was both a butchers and Municipal slaughterhouse. The original building was built in 1547 during the reign of Charles V and was located outside the city walls. In the 1960s it was rebuilt in the newly reformed Plaza del Pópulo. As the original building was longer than the new Plaza de Pópulo the ends were "folded" back to the sides.  

Although archaeological samples do not suggest the presence of many human settlements in the area prior to the Copper Age (middle of the III Millennium BC), there is evidence dating back to the fifth Millennium BC documenting the life habits of the hunters and gatherers of epipalaeolithic groups. A thousand years later, communities from further south arrived, specifically from the caves and shelters of Sierra Mágina, bringing with them Neolithic forms based on agricultural activity and certain technical advances such as the polishing of stone and ceramics. This has been documented in sites such as Los Horneros, Los Morales and Toya.

Baza Musem features a selection of artefacts on display that show different periods of human occupation in Baeza. From the Medieval Period, a distinction is made between the Arab civilization (Almohad invasion) and the Christian period following the reconquest. From the Modern Era doors, keys, chests, safes, portraits are on display.