I bought my car to Ukraine in November 2017. The initial process of bringing the car into the country is quite straight forward.
I arrived from Poland, around 6pm on a Sunday evening. There were a few cars ahead of me, so the queues were quite short. An official asked to see the paperwork for my car and check inside. She checked the contents of my car and asked where I was going.
I then proceeded to the control point. This is where you get a stamp on a piece of paper for immigration and another one for customs. I did not have to pay any fees and I was sent on my way. The whole process took around 30-40 minutes to complete.
With my car in Ukraine, I looked into the possibility of importing it. It was a 2013 Audi A3 1.4 TFSI. So, fairly small engine and has very low emissions. But, the cost to import would be approximately $5000. The car (in the UK) was only worth around $12000, so it did not make financial sense to import it. Especially, as the car was right hand drive.
So, I decided to take it back to the UK and sell it there. But, leaving Ukraine was a lot more difficult. It took over 6 hours to get through the same crossing. There were more people trying to leave at 9pm on a Saturday night and the process seemed to take much longer to get my stamps required.
I decided that it is much better to buy a car in Ukraine, compared with trying to import one. I have heard that you can keep a car in Ukraine for 12 months before needing to import it. Some people simply take the car over the boarder for a day or two and then return with it. I hear this resets the 12 month requirement. I don't want the hassle. Cars are more expensive in Ukraine, but I'd prefer to pay an extra couple of thousand dollars and have a legal, legitimate car, rather than face any issues with police or border controls.