  This article reviews experimental work on the ultrafast electron dynamics in
the topological surface state (TSS) of three-dimensional (3D) topological
insulators (TIs) observed with time- and angle-resolved two-photon
photoemission (2PPE). The focus is laid on the generation of ultrafast
photocurrents and the time-resolved observation of their decay. 2PPE not only
allow to unambiguously relate the photocurrents to the spin-polarized
electronic surface states. Probing of the asymmetric momentum distribution of
the electrons carrying the current makes it possible to study the microscopic
scattering processes that governs the unusual electron transport in the time
domain. Ultrashort mid-infrared pump pulses permit not only a direct optical
excitation of the TSS in Sb$_2$Te$_3$ but also lead to a strong asymmetry of
the TSS population in momentum space. Two-dimensional band mapping of the TSS
shows that this asymmetry is in fact representative for a macroscopic
photocurrent while the helicity-dependence of the photocurrent is found to be
small. The time-resolved observation of the photocurrent decay reveals a huge
mean free path of the electrons in the TSS.
