SkyNet kept sending back terminator robots in human biological casings, and various members of the Connor family kept destroying them.
“It got smart,” was what Kyle Reece had said, but how smart is a musclebound terminator robot speaking in an Austrian accent?
So, after a while (which is a strange phrase to use when you’re dealing with time travel and paradoxes), SkyNet really did get smart. It stuffed a dog with Von Neumann nanobots and bangs it into the past.
The nanobots spilled out of the dog, built quintillions of copies of themselves, and took over the world.
The end.