Strata Florida was founded by Cistercian Monks in the year 1164 CE, the Abbey's chapel was consecrated much later in the year 1204. The Cistercian Monks at Strata Florida eventually became quite wealthy and influential Ystrad Fflw had arguably become the cultural center of medieval Wales. Among the great works that were produced here were the Brut y Tywysogion (one of the first chronicles of Welsh History written in the Welsh Language) and the ballad of Mabinogion. One of the foremost poets of the middle ages, Dafydd ap Gwilym was known to have lived and compiled his works inside Strata Florida. Strata Florida was so important in the political and cultural spheres of Wales that the Welsh princes, including the famous Llywelyn the Great often held council there to decide the major political issues of the day.
Unfortunately the prosperity and influence of the Cistercian Monastery began to decline following the English conquest of Wales in 1277 CE. Perhaps this is representative of the decline of Welsh culture in general, the confiscation of Welsh lands under English nobles styled "Marcher-Lords" marks the beginning of the gradual Anglicization of Wales. This period marks the beginning of the troubles that the Cistercian Monks of Strata Florida faced during the tail-end of the Middle Ages.
A 16th century portrait of Henry IV
During the Welsh war of Independence the problems faced by the Abbey grew worse. In 1401 the English King Henry IV and his son lead an army in pillaging Strata Florida, after the monks there were found to be sympathetic to the Welsh rebel leader, Owain Glyndŵr. Following this incident the monks were expelled from the Abbey. Strata Florida was used as an English military base for the remainder of the war. In 1415 following English victory in the Glyndŵr rising the Abbey was returned to the Cistercian Order, though the monks would never truly recover from the devastation incurred upon them during the conflict.
Henry VIII
The protestant reformation and the rise of Anglicanism in England would mark the final death of Strata Florida. In the 1540's Henry VIII the founder of Anglicanism assumed direct control over religion in England. As a consequence of this many monasteries including Strata Florida Abbey were plundered and destroyed by English Soldiers, often being converted into manor houses for use of the nobility.
Sources:
http://www.bbc.co.uk/blogs/waleshistory/2012/07/strata_florida_abbey.html
http://strataflorida.org.uk/
https://www.historic-uk.com/HistoryUK/HistoryofWales/The-English-conquest-of-Wales/