Harmony with Scotland, the career of Llewellyn the Great, the loss of Poitou. During the minority of Henry, English prestige and power was at something of a low point - with the one exception of Gascony, where a supreme effort brought one success. And meanwhile in Southern France, the Cathars burned.
Llewellyn the Great
Llewelly was both a warrior and consummate politician. He had a vision for a Wales united under one ruler (himself, in case you were wondering). And although Henry manged to hang on to the principle that other rulers of Wales should pay him homage, Llewellyn pretty much achieved the fact of a united Wales. After his death in 1240, historians point to the lack of lasting legacy, but for 40 years Llewellyn dominated Welsh politics and more than held the English at bay.
The loss of Poitou
Hubert de Burgh knew that the English were in a perilously weak position in Poitou - no cash, no power. But for a while they managed to get Phillip Augustus to renew the truces. Meanwhile they had to keep the powerful Lusignan clan happy in La Marche, going to the extent of betrothing little 10 year old Joan, daughter of John, to Hugh de Lusignan.
Isabella of Angouleme left England and her son for her homeland; and then in 1220 dropped a bombshell. She stuck her palm in her daughter's face, pushed hard, and married Hugh de Lusignan herself, son of the man she had been betrothed to before John had come along.
Then in 1224, Louis the new king of France did not renew the truce, and made alliance with Hugh and Isabella. By 1225 it was all over, Poitou was gone, and it looked like Gascony would go the same way - only Dax, Bayonne and Bordeaux held out.
Louis left hugh to mop up - after all there were only 3 major towns holding out. But in fact the Gascons were determined to stay with England - afterall, that's where all their trade went. So they maintained and army in the field, and Henry managed to raise a tax.
So in 1225 William of Salisbury and Richard of Cornwall came over, and soon Hugh found himself pushed back to a few areas, including the town of La Reole. Louis tried to come back and help, but was ambushed trying to cross the Dordogne, and therefore unable to link up with Hugh.,
By the end of 1225, therefore, Gascony had been saved for the English crown for 200 years more.