Madog ap Maredudd possessed Powys within its boundaries, from the Perfedd to Gwaun in the uplands of Arwystli
The opening sentence of the The Dream of Rhonabwy from the Mabinogion. 1
A Welsh cantref comprising the land of the headwaters of the rivers Severn and Wye divided into the two commotes of Arwystli Uwchcoed and Arwystli Iscoed 2 and traditionally forming part of the kingdom of Powys. Possibly named after Arwystli Hen (Aristobulus the Old), a semi-mythic character who was supposedly one of first missionaries to bring Christianity to Britain.
Its location at the extreme south western corner of Powys, on the borders with Meirionydd (the latter generally under the control of the kings of Gwynedd), gave it a certain strategic importance as the route through which the kings of Powys could seek to impose themselves upon Meirionydd. (And vice-versa of course.)
Arwystli had its own rulers or tywysogion; minor sub-kings owing fealty to whichever overlord was most powerful at the time, typically those of Powys. The most notable of these was one Trahaern ap Caradog, who was related to both Bleddyn ap Cynfyn and Grufudd ap Llywelyn, and therefore managed to succeed to the throne of Gwynedd in 1175, and ruled until his death in 1081.
Following the final fall of Gwynedd in 1283, Arwystli became a Marcher Lordship. The Normans established the town of Llanidloes as a centre of government for the area. After the Acts of Union (1536-1543) it formed part of the newly created county of Montgomeryshire. Following which there was a significant in-migration of English families to Montgomeryshire in general and to the lordship of Arwystli in particular 3, who inter-married with, and were eventually absorbed by, the local Welsh population and left behind a legacy of English sounding surnames to confuse later generations of genealogists and historians.
NOTES
1 The Lady Charlotte Guest translation reads "Madawc the son of Maredudd possessed Powys within its boundaries, from Porfoed to Gwauan in the uplands of Arwystli." But I know what she means.
2 Literally Arwystli 'above the trees', that is forest, and 'below the trees'.
3 Related to the fact that Robert Dudley, Earl of Leicester was granted a number of lordships in Wales by Elizabeth I, including Arwystli and Cyfeiliog in Montgomeryshire and Chirk, Chirkland and Denbigh in Denbighshire. See "An English Settlement in Western Montgomeryshire during the Tudor Period" by Murray Chapman from the Montgomeryshire Collections of the Powysland Club (1999)