Classification of Hilbert functions of Artinian algebras with additional properties, like Gorenstein or complete intersections, plays an important role in singularity theory and in algebraic geometry. The sequences that occur as the Hilbert functions of standard graded complete intersections are well understood classically thanks to Macaulay and Stanley. Very little is known in the local case except in codimension two. In this talk we will discuss the Hilbert functions of local complete intersections.