For arbitrary commutative Rota-Baxter algebras, proper exponential solutions of fixpoint equations are described by what is known as the classical Spitzer identity. The classical Bohnenblust-Spitzer identity involves the symmetric group and set partitions. It generalizes the simple observation that the n-fold iterated integral of a function is proportional to the n-fold product of the primitive of this function. In earlier work we have generalized the seminal Cartier-Rota theory of classical Spitzer-type identities to noncommutative Rota-Baxter algebras. Pre-Lie algebras play a crucial role in this approach. In this talk we present new work on Spitzer-type identities, which is based on fine properties of pre-Lie algebras. I will provide a short review of background material to make the talk reasonably self-contained.