  Topological insulators offer unique opportunities for novel electronics and
quantum phenomena. However, intrinsic material limitations often restrict their
applications and practical implementation. Over a decade ago it was predicted
that a time-periodic perturbation can generate out-of-equilibrium states known
as Floquet topological insulators (FTIs), hosting topologically protected
transport and anomalous Hall physics, and opening routes to optically tunable
bandstructures and devices compatible with petahertz electronics. Although such
states have not yet been directly observed, indirect signatures such as the
light-induced anomalous Hall effect were recently measured. Thus far, much
remained experimentally unclear and fundamentally unknown about solid-state FTI
and whether they can be employed for electronics. Here we demonstrate coherent
control of photocurrents in light-dressed graphene. Circularly-polarized laser
pulses dress the graphene band structure to obtain an FTI, and phase-locked
second harmonic pulses drive electrons in the FTI. This approach allows us to
measure resulting all-optical anomalous Hall photocurrents,
FTI-valley-polarized currents, and photocurrent circular dichroism, all
phenomena that put FTIs on equal footing with equilibrium topological
insulators. We further present an intuitive description for the
sub-optical-cycle light-matter interaction, revealing dynamical symmetry
selection rules for photocurrents. All measurements are supported by strong
agreement with ab-initio and analytic theory. Remarkably, the photocurrents
show a strong sub-cycle phase-sensitivity that can be employed for ultrafast
control in topotronics and spectroscopy. Our work connects Floquet and
topological physics with attoscience and valleytronics, and goes beyond band
structure engineering by initiating lightwave-driven dynamics in FTI states.
