The representation of integers by binary forms

Let F(x , y) be an irreducible binary form of degree at list 3 and with integer coefficient. Then by a well-known result of Thue the equation F(x , y) = m has only finitely many solutions in integers x and y. I shall discuss some different methods from classical Diophantine analysis and the Geometry of numbers to give upper bounds for the number of solutions to such equations.