The article recapitulates the economic analysis of poverty and famines proposed by Amartya Sen, an Indian economist who was awarded a Nobel Prize in 1998. Part 1 of the article consists of introductory remarks. Part 2 presents basic concepts relating to Sen’s social philosophy and theory of poverty with special reference to the entitlement approach. Arguments have been presented to prove that famines occur when at one time many people in a country suffer from entitlement failures. Indirectly, a thesis is implied that poverty-stricken abilities which allow to satisfy basic needs or to "achieve valuable functionings" should set the area for evaluation of inequalities. Part 3 of the article is an enlargement on Amartya Sen’s theory on poverty and famines themselves (problems of identifying poverty and aggregation of features making up poverty), as well as a presentation of appropriate statistical measures of poverty (including the so- called Sen’s index). An outline of features of contemporary famine, which due to the paradoxes involved with it has become a separate research category, provides an indispensable background for the entitlement approach presented in the article. A strong emphasis has been put in the article on the fact that Sen strongly challenges the view according to which a shortage of food is the main, or only, explanation for famine.