Experts and BHG readers answer.
weeds and clover along blacktop driveway
The soils next to driveways are often shallow because contractors must lay down a thick road base of gravel to support the driveway. This road base typically extends out beyond the blacktop or concrete. Tilling up the area and working in organic matter is one means of creating a better rooting zone for grass. You may also want to consider growing a drought tolerant groundcover such as creeping thyme next to the driveway.