The border is about 1,900 miles (3,100 km) long and traverses all sorts of terrain.
Mr Trump says his wall will cover 1,000 miles and natural obstacles will take care of the rest.
But how much will it cost and who is going to foot the bill?
What is the estimated budget?
“I would build a great wall, and nobody builds walls better than me, believe me, and I build them very inexpensively.”
Mr Trump claims the total cost of the wall will be $10bn (£7.5bn) to $12bn. But estimates from fact checkers and engineers seem to be universally higher.
Senate Majority Leader Mitch McConnell estimated it will cost between $12-15bn, as he addressed reporters at a Republican conference in Philadelphia.