Klingons are one of the most barbaric and less technologically advanced races in the Star Trek universe, and they typically prefer to solve problems with combat actions rather than words.
So how did a race who spends too much time yelling, fighting and feuding and not nearly enough time studying, experimenting or inventing manage to create a warp drive?
According to this comic from Sheldon Comics they got it from that one Klingon who was super into science, the one who has a pencil tucked behind his ear instead of a knife.
-Via Geeks Are Sexy
But there must be other races of the empire who stay at home and do the sciencing, the farming, the ship-building, the uniform-sewing, etc. We just haven't seen them on TV.