|Pope Paschal II speaking to Anselm of Canterbury|
Like other popes, he had to deal with the controversy over investiture; in his case, specifically, he weighed in on England's trouble between King Henry I and Archbishop Anselm of Canterbury, finding the same solution later settled in the Concordat of Worms: agree that the pope names clergy and confers religious titles, but the king of England can confer secular titles and grant land.
As for the relations between Paschal and the Holy Roman Emperor: Henry V proved to be more difficult in some ways than his father had been, even marching an army into Italy against Paschal over the Investiture Controversy. Paschal had to agree to give up all properties and possessions it had received since the days of Charlemagne. Only for this would Henry give up his "rights" of investiture. The agreement was to take place in February 1111, but the Romans objected very strongly to a German army trying to change the status quo: they revolted, and Henry retreated, but not before capturing Paschal and 16 cardinals! The pope was imprisoned for two months; a rescue mission by Robert I of Capua with 300 men failed. Paschal was released after agreeing to allow Henry to invest priests and bishops. (Months later, with Henry safely back across the alps, a council and Paschal would excommunicate him for his actions.)
Paschal also had the opportunity during his reign to unite the Catholic (Western) and Orthodox (Eastern) churches; Emperor Alexios I was willing. Paschal, however, laid down the condition that the pope be seen as the ultimate ruler of all churches throughout the world, and this the Patriarch of Constantinople would not agree to.
One of Paschal's appointments in 1112 was of a priest named Erik Gnúpsson to be Episcopus Groenlandia regionnumque finitimarum ["Bishop of Greenland and nearby regions"]. Norseman had settled Greenland in the 10th century, and there was another land to the west called "Vinland," which was almost certainly Newfoundland. This gives Paschal the privilege of having appointed the first bishop of the Americas. (Gnúpsson left for Vinland in 1121 and never returned, alas.)*
*Vatican and Icelandic records both mention this; see These Stones Bear Witness, by Richard White for more on the Norse presence in North America.