Let F(x,y) be a binary form of degree at least 3, and with integer coefficients. We will show that the equations of the form F(x,y) = 1, often have no integer solutions in x, y. More precisely, we will show that a positive proportion of integral binary cubic forms that locally everywhere represent 1, do not globally represent 1. We order all classes of binary cubic forms by their absolute discriminants. We will prove the same result for binary forms of any degree at least 3, provided that these forms are ordered by the maximum of the absolute values of their coefficients. This is a joint work with Manjul Bhargava.