Radnorshire (Welsh: Sir Faesyfed) was one of the thirteen counties of Wales that existed from 1536 until their abolition in 1974, later becoming a district of Powys from 1974 to 1996. It covered a sparsely populated area, and was bounded to the north by Montgomeryshire and Shropshire, to the east by Herefordshire, to the south by Brecknockshire and to the west by Cardiganshire.

The county was formed in 1536 from several Marcher lordships under the Laws in Wales Acts, as part of the formal annexation of Wales into the Kingdom of England by Henry VIII. The county was named after New Radnor, which was the original county town. From 1543 onwards the assizes were held alternately at New Radnor and Presteigne, later settling at Presteigne alone. Presteigne then served as the county's administrative centre until 1889 when Radnorshire County Council was established and chose to base itself in Llandrindod Wells instead.

The administrative county was abolished in 1974, with the area becoming the lower-tier Radnor district within the new county of Powys. The district was renamed Radnorshire in 1989. Radnorshire District Council was abolished in 1996 when Powys became a unitary authority. Powys County Council then had a Radnorshire "shire committee" until 2018.

The largest town in Radnorshire was Llandrindod Wells, with other towns being Knighton, Presteigne, and Rhayader. The Radnor Forest is an area of high ground covering a large part of the east of former county.

The geographic territory of what was Radnorshire roughly corresponds with the Welsh territory of Rhwng Gwy a Hafren (English: Between Wye and Severn) which fell under the control of the Marcher Lords at the end of the 11th century. The area that would become Radnorshire included Cwmhir Abbey, a Cistercian monastery founded in 1176 at Abbeycwmhir. The Battle of Bryn Glas was fought on 22 June 1402 at Pilleth during the rebellion of Owain Glyndŵr.

Until the Laws in Wales Act 1535, Radnor was outside the Principality of Wales. This peculiar Marcher status and its wont of Welsh speakers gave weight to the traditional local expression, "Neither Wales nor England, just Radnorsheer"

The 1535 act created Radnorshire from a number of former territories, including the cantrefs of Maelienydd and Elfael and the commotes of Gwrtheyrnion and Deuddwr. The act also specified that New Radnor was the county town, and directed that the county's assizes and quarter sessions should be held alternately at New Radnor and Rhayader. A judge was murdered at Rhayader a few years later, highlighting the dangers to English judges in that part of the county. In 1543 the law was changed, directing that the assizes should no longer be held at Rhayader, but should instead alternate between New Radnor and Presteigne. The practice of holding sessions alternately at New Radnor and Presteigne later gave way to all sessions being held at Presteigne.

The county's poverty was remarked upon thus in the 17th century by an anonymous visitor: