If you want to carry your ride on your car, the right rack carrier will do it. As Queen put it...
"I want to ride my bicycle,
I want to ride my bike.
I want to ride my bicycle,
I want to ride it where I like."
- Freddie Mercury, amateur cyclist.
There are several ways to put bikes on top of the car. Each has distinct advantages and disadvantages.
First is the fork mount, which means you take the front wheel off and attach the bike to your rack primarily using the fork. The stray wheel goes on a wheel fork or in the back of your car or truck.
The benefit of a fork mount is that it's totally solid, as you're locking down one of the strongest parts of the bike directly to the rack and thus to the car itself, so the bikes don't budge. The downside is you have to remove the front wheel when you use them. These days on most bikes that's a no brainer due to quick release. But you also have to find a place for the front wheel...no biggie, unless you put your front tire in the car on a hot day and it pops due to pressure increase (we know from experience).
The frame mount grabs the frame's down tube. It's good and simple, doesn't require disassembling the bike, but does mean you have to lift the entire bike up on the car, which is sometimes tricky, and isn't so good for oversized or carbon-fiber tubing. A lot of folks use these on the top of pop-up campers, as getting the bike up and down is easier, and once the bike is down it doesn't require reassembly.
The final top-of-car solution has been on the front of many city buses for years. That's the wheel mount. Wheel mounts grab the front wheel between two arms and hold it tight, and quickly too. Disk brakes are not an issue, and wheel sizes from 20" to 29" all work fine. Also bikes with suspension, especially one with the one-armed forks are not a problem.
That's it for on-top. If you have questions, feel free to write and ask for more information. We hope this helps.