One side of the controversy holds that the ultimate cause of the extinction of the dinosaurs was:

Extrinsic: meaning of an extraterrestrial nature, and Catastrophic: meaning sudden and devastating

One main hypothesis with variations exists today.

The Alvarez Hypothesis:

The main hypothesis was proposed in 1980 by (among others) Luis and Walter Alvarez of the University of California at Berkeley. The original Alvarez hypothesis is the basis for several subsequent variations on the theme that a large extraterrestrial object (asteroid or comet) collided with the Earth, its impact throwing up enough dust to cause the climatic change. No crater was originally found, but it was assumed that one existed that was about 65 million years old and 100 kilometers (about 65 miles) in diameter.

ARGUMENT #2: Asteroids and similar extraterrestrial bodies are higher in iridium content than the Earth's crust, so they figured that the iridium layer must be composed of the dust from the vaporized meteor.

ARGUMENT #3: Shocked quartz is present in the rocks of the 65 million year old geological boundary (indicating a violent tremor that cracked the quartz grains).

ARGUMENT #4: The presence of glassy spheres that look like impact ejecta (molten rock that solidified into droplets when cooled) in the 65 million year old geological boundary.

ARGUMENT #5: A soot layer was found in many areas (evidence for widespread forest fires).