Based on social media profiles apparently belonging to them, the brothers were interested in militancy, Islam and Chechnya, a region in Russia.
The two reportedly came to the United States as refugees in the early 2000s, perhaps a couple of years apart, after fleeing the violence in the Caucasus. Both appeared to maintain close ties to their ethnic homeland. The younger brother, Dzhokhar, included the seal of his hometown soccer team as the background of his Twitter account. The older, Tamerlan, expressed his hope for Chechen independence and included books about Chechnya about on his Amazon wish list.
The brothers were also practicing Muslims, posting messages about Islam and Ramadan on various social media profiles. There is an indication that Tamerlan may have had a more radical streak, reflected in his YouTube playlist featuring videos by a radical cleric living in Australia and videos about joining an Islamic army to help establish a Caliphate as well as a playlist on “Terrorists” (the videos of which had previously been deleted by YouTube).
A more complete profile on the brothers can be found here: Social Media Profiles Shed Light on Brothers Accused in Boston Marathon Attack.