The concept of the Eisenstein ideal in Hecke algebras of classical modular curves was introduced by Mazur in the 1970's. As was demonstrated by Mazur, Ribet, Wiles and others, the Eisenstein ideal provides a powerful tool in many arithmetic problems over number fields. We will discuss the analogue of the Eisenstein ideal in the context of Drinfeld modular curves, and some of its applications to the study of rational torsion subgroups, component groups and cuspidal divisor groups of Jacobians of Drinfeld modular curves.