Brougham Castle (pronounced /ˈbruːm/) is a medieval building about 2 miles (3.2 km) south-east of Penrith, Cumbria, England. The castle was founded by Robert I de Vieuxpont in the early 13th century. The site, near the confluence of the rivers Eamont and Lowther, had been chosen by the Romans for a Roman fort called Brocavum. The castle, along with the fort, is a scheduled monument: "Brougham Roman fort and Brougham Castle".

In its earliest form, the castle consisted of a stone keep, with an enclosure protected by an earthen bank and a wooden palisade. When the castle was built, Robert de Vieuxpont was one of the only lords in the region who were loyal to King John. The Vieuxponts were a powerful land-owning family in North West England, who also owned the castles of Appleby and Brough. In 1264, Robert de Vieuxpont's grandson, also named Robert, was declared a traitor, and his property was confiscated by Henry III. Brougham Castle and the other estates were eventually returned to the Vieuxpont family, and stayed in their possession until 1269, when the estates passed to the Clifford family through marriage.

With the outbreak of the Wars of Scottish Independence, in 1296, Brougham became an important military base for Robert Clifford, 1st Baron de Clifford. He began refortifying the castle: the wooden outer defences were replaced with stronger, more impressive stone walls, and a large stone gatehouse was added. The importance of Brougham and Robert Clifford was such that, in 1300, he hosted King Edward I at the castle. Robert's son, Roger Clifford, was executed as a traitor, in 1322, and the family estates passed into the possession of King Edward II, although they were returned once his son Edward III became king. The region was often at risk from the Scots, and in 1388, the castle was captured and sacked.

Following this, the Cliffords began spending more time at their other castles, particularly Skipton Castle in North Yorkshire. Brougham descended through several generations of Cliffords, intermittently serving as a residence. However, by 1592, it was in a state of disrepair, as George Clifford, 3rd Earl of Cumberland was spending more time in southern England due to his role as Queen's Champion. The castle was briefly restored in the early 17th century, to such an extent, that King James I of England was entertained there in 1617. In 1643, Lady Anne Clifford inherited the estates, including the castles of Brougham, Appleby, and Brough, and set about restoring them. Brougham Castle was kept in good condition for a short time, after Lady Anne's death in 1676; however, Thomas Tufton, 6th Earl of Thanet, who had inherited the Clifford estates, sold the furnishings in 1714. The empty shell was left to decay, as it was too costly to maintain. As a ruin, Brougham Castle inspired a painting by J. M. W. Turner, and was mentioned at the start of William Wordsworth's poem The Prelude, as well as becoming the subject of Wordsworth's Song at the Feast of Brougham Castle upon the Restoration of Lord Clifford, the Shepherd, to the Estates and Honours of his Ancestors. The castle was left to the Ministry of Works, in the 1930s, and is today maintained by its successor, English Heritage

The site of Brougham Castle has been fortified since the Romans erected the fort of Brocavum at the intersection of three Roman roads. With the rivers Eamont and Lowther flowing nearby and meeting to the west, the site had natural defences and the area was fertile and easy to cultivate. A civilian settlement grew around the fort. When Angles arrived in the area they named the place Brougham, meaning "the village by the fort". Between the end of Roman rule in the early 5th century and the Norman Conquest in the late 11th century, Cumbria was a turbulent area. Although the site was a defendable position, there is no evidence that Brougham was refortified during this time. In 1092, William II (also known as William Rufus) captured Cumbria south of the Solway Firth and established a new border far north of Brougham. The site at Brougham remained unfortified. Carlisle Castle secured the border, and castles at Appleby and Brough, both south east of Brougham, protected the line of communication from Carlisle to Yorkshire. In 1203, the Barony of Westmorland – containing Appleby, Brough, and Brougham – was granted to Robert de Vieuxpont by King John. A favourite of John's, Vieuxpont was one of only a few lords loyal to him in northern England, whose inhabitants became so discontented with the king's rule that they eventually rebelled. Around 1214, Vieuxpont asserted control over more land, including half the manor of Brougham. It was in this atmosphere of unrest that Brougham Castle was founded.

Vieuxpont was one of only a few supporters of the king in northern England, and he most likely began construction of Brougham Castle as soon as he acquired the land. At this stage, the castle would have been enclosed by an earthen bank surmounted by a timber palisade. The first three storeys of the stone keep date from this period. It was entered through the first floor via a forebuilding. To the east of this was a stone structure which was probably a hall. Building in stone was an expensive and time-consuming process. No records tell us how much Brougham cost to construct, but there are records for other stone construction. For example, the late-12th-century stone keep at Peveril Castle in Derbyshire would have cost around £200, although something on a much larger scale, such as the vast Château Gaillard, cost an estimated £15,000–20,000 and took several years to complete.

In 1216, when a Scottish army invaded the Eden valley and Alan of Galloway occupied Westmorland, Brougham Castle played no part in the county's defence, probably because it was unfinished. Construction would have been suspended until Alan retreated in 1217. Vieuxpont received control over the king's revenues from Cumberland, and these helped fund the construction of the castle. Brougham Castle was constructed in the northern part of the old Roman fort, and stone from the ruins was probably used to help build the castle. When Robert de Vieuxpont died in 1228, his only son – John – was a minor, so his property was taken into the care of a warden.

John de Vieuxpont died in 1241, before he came of age. The new heir, John's son Robert, was not old enough to inherit, so the family's lands remained in wardship. During this time, the estates fell into disrepair, and this probably included Brougham Castle. When Robert de Vieuxpont came of age in around 1257 he inherited considerable debts. He was one of the northern lords that revolted in support of Simon de Montfort in the Second Barons' War (1264–1267). By June 1264, Vieuxpont was dead; as he was considered a traitor, his property was confiscated by King Henry III. In 1266, the king pardoned Vieuxpont posthumously, and his two daughters inherited the family estates. The guardians of the two girls, who at the time were too young to marry, divided the Vieuxpont lands with the expectation that they would come into their possession through marriage. Isabel Vieuxpont was given in marriage to Roger Clifford, the son of her guardian, and with her the shrievalty of Westmorland and the castles of Brougham and Appleby transferred to the Cliffords.