The 9th century opened with a major war in the north-east where Carolingians threw Muslims out of what is now Old Catalonia. The death of emir Hisham in Cordoba started a major civil war where local elites (mostly of Muwallad stock, i.e. local Roman-Iberian-Visigothic converts to Islam) appealed to Franks for help. Charlemagne's son, king of Aquitaine and future emperor Louis the Pious crossed with his army into Spain in 800. After a long siege they took Barcelona (801) and made it capital of a Carolingian county that would be the HQ of further conquest and frontier defence. There were several failed attempts to take Tortosa, the next logical target to the south. At the same time, clashes between Franks, Cordobans and the two local Basque factions in the upper Ebro led to the creation of a Christian kingdom of Pamplona, closely allied with the Muslim rulers of the Banu Qasi family against both Franks and, occasionally, Cordoba (see my comment here). In 813, Christians took the fight to the sea, ambushing an Andalusi fleet off Mallorca as it was coming back from an attack on Corsica.

For the rest of the century, there were numerous Andalusi raids against Barcelona and Girona, mostly in conjunction with local revolts against the Franks or with Frankish infighting. Even though they even managed to take and sack the city in 851 or 852, Barcelona remained in Frankish hands. Local counts gained independence towards the end of the century with the Carolingian collapse and continued skirmishing with Muslims on their own.

As to Asturias, even though their chroniclers would later invent stories of some major battles, we have no evidence anything important actually happened. It was more of a process of gradual consolidation and settlement of abandoned lands they took over. The most important thing they tried to do was resettle the abandoned Roman city of Leon - that the Cordobans duly burnt to the ground in 846. It was resettled ten years later.

Most of 9th century Asturian chronicles I saw were mostly concerned with interpreting how Visigothic kingdom had come to ruin through their sins and how Asturias was the true heir and their kings would be throwing the infidels out shortly. Conquerors and Chroniclers of Early Medieval Spain by Kenneth Baxter Wolf (Liverpool, 1990) is a good introduction.

EDIT: Oh, and the 1995 thesis by John Wreglesworth, available online [here] (http://etheses.whiterose.ac.uk/535/), goes into great detail on Asturian sources.