We study the homotopy type of complete intersections. These are complex manifolds of complex  dimension n embedded in complex projective space as the common zeros of k polynomials in the complex  projective space of dimension n+k.The diffeomorphism type only depends on the degrees of the polynomials. The total degree is the product of these degrees.. It is a homotopy invariant. We determine necessary and sufficient conditions for two complete intersections of the same dimension  and total degree to be of the same homotopy type for dimensions n larger than the total degree. We also discuss the problem of diffeomorphism type for complete intersections.