  Context. The prototypical low-mass young stellar object, T Tauri, is a
well-studied multiple system with at least three components. Aims. We aim to
explore the T Tau system with the highest spatial resolution, study the time
evolution of the known components, and re-determine the orbital parameters of
the stars. Methods. Near-infrared classical imaging and integral field
spectrograph observations were obtained during the Science Verification of
SPHERE, the new high-contrast imaging facility at the VLT. The obtained FWHM of
the primary star varies between 0.050" and 0.059", making these the highest
spatial resolution near-infrared images of the T Tauri system obtained to date.
Results. Our near-infrared images confirm the presence of extended emission
south of T Tau Sa, reported in the literature. New narrow-band images show, for
the first time, that this feature shows strong emission in both the Br-{\gamma}
and H2 1-0 S(1) lines. Broadband imaging at 2.27 {\mu}m shows that T Tau Sa is
0.92 mag brighter than T Tau Sb, which is in contrast to observations from Jan.
2014 (when T Tau Sa was fainter than Sb), and demonstrates that T Tau Sa has
entered a new period of high variability. The newly obtained astrometric
positions of T Tau Sa and Sb agree with orbital fits from previous works. The
orbit of T Tau S (the center of gravity of Sa and Sb) around T Tau N is poorly
constrained by the available observations and can be fit with a range of orbits
ranging from a nearly circular orbit with a period of 475 years to highly
eccentric orbits with periods up to 2.7*10^4 years. We also detected a feature
south of T Tau N, at a distance of $144 \pm 3$ mas, which shows the properties
of a new companion.
