The Q were a mysterious race of virtually omnipotent and omniscient "higher-beings" who made up, and were governed by, the Q Continuum.
To interact with the 3-D realm, the Q presented themselves in the guises of the species they interacted with, and were readily able to change the appearance of their avatars. (TNG episodes: "Encounter at Farpoint", "Hide and Q", TOS - The Q Gambit comic: "Part 3")
Nonetheless, the Q were powerful enough to teleport across vast distances, "misplace" asteroid belts, collapse galaxies, and even travel outside of the universe. (TNG episodes: "Q Who", "Deja Q", "True Q")
Sufficiently powerful entities could pose threats to the Q however with the forces of 0, The One, Gorgan, and (*), bringing the Q to their knees. The latter two were even able to evade capture by their foes. (TNG novel: Q-Strike)
Equally, when forced into a war with the Pah-wraiths, the Q were brought to the brink of defeat, with Q even confessing to Kirk that, in their native dimension, the Q were not the gods they were in the 3-D universe but as mortal as humans. Being at the nexus of the Bajoran wormhole, an interdimensional crossroads, stripped Q of his powers. (TOS - The Q Gambit comics: "Part 5", "Part 6")
Likewise, though they regarded themselves as more powerful than the Organians, Metrons, or even Prophets, all three races proved capable of fighting the Q on equal footing with a war between them projected to last centuries. (TNG - The Q Conflict comics: "Issue 4", "Issue 5", "Issue 6")
Despite interacting with less evolved species across time and space, the Q culture was heavily stagnant and sterile that by the 21st century, Quinn felt he had done and seen literally everything in the universe. (VOY episode: "Death Wish")
During the Q Civil War, the more conservative Q sought to end interaction with other species as a way of preserving this culture while the other faction sought to bring change to their race. (VOY episode: "The Q and the Grey")