Poverty policy in the United States has come about mainly as the result of initiatives put forth by two presidents in the 20th century. The two presidents who created the basics of the modern approach to poverty were Franklin D. Roosevelt and Lyndon B. Johnson.
Before the Great Depression and the New Deal, there was really nothing in the way of federal policy on poverty. It was not seen as something the government was supposed to be involved in. But then came the Depression. After the Depression hit, there was much more of an attitude that the government should be involved in ending poverty. This led to a number of programs aimed at helping those who had become poor.
In the 1960s, Pres. Johnson expanded this idea. His "War on Poverty" created more federal programs that were meant to end poverty by giving money to poor people and by trying to help them get out of poverty through job training, early childhood education, and the like.
The sorts of programs created by Roosevelt and Johnson form the basis of poverty policy today.