If A is a commutative ring, its primitive ideals are just its maximal ideals, in other words, they form the maximal spectrum of A. Describing the maximal spectrum goes back to the classics of algebra from the beginning of the 20th century. If U is a noncommutative ring, its primitive ideals are defined as the annihilators of simple U-modules. If U is an enveloping algebra of a finite-dimensional simple Lie algebra such as g=sl(n,C), then the primitive ideals of $U$ are described by a celebrated theorem of Duflo, and have been further studied by Borho, Joseph, and others. In this talk, I will describe the recent results of Alexey Petukhov and myself, providing a complete description of the integrable primitive ideals of the universal enveloping algebras of the Lie algebras sl(\infty), so(\infty), and sp(\infty). Moreover, we have recently proved that any primitive of U(sl(\infty)) is integrable, obtaining in this way an explicit description of the primitive ideals of U(sl(\infty)). Our results are based in particular on the pioneering work of A. Zhilinskii from 1990s.