If you search online for ways to remove oil stains, you'll come across all kinds of things. One of the most common suggestions I've come across from "experts" is to use a brick to grind cat litter into the concrete. This does absorb wet oil on the top of the concrete, but it doesn't really get rid of the stain.
The best solution is cool product called Pour-N-Restore. It goes on as a liquid and dries into a powder. The company's website claims that the product soaks into the concrete and pulls up embedded oil stains, capturing them in the dry powder. Whatever it does, it works! I've used it several times on my driveway and I can't even tell where the stains were.
Another cool thing about this product is that you're not rinsing oily slime off the driveway into the grass or down a drain. Pour-N-Restore holds the oil in the powder, so you just sweep it all up. The back of the label also states that it's biodegradable and phosphate-free.
Step 1: Sweep
After Pour-N-Restore dries out, you just sweep up the powder. Sometimes, after you sweep, the concrete will still be wet. You just need to let this moisture evaporate.
Step 2: Oil stain is gone
You can see that the oil stain is gone now. All the oil is trapped in the white powder.