  Context. Taurus represents an ideal region to study the three-dimensional
distribution of the young stellar population and relate it to the associated
molecular cloud. Aims. The second Gaia data release (DR2) enables us to
investigate the Taurus complex in three dimensions, starting from a previously
defined robust membership. The molecular cloud structured in filaments can be
traced in emission using the public far-infrared maps from Herschel. Methods.
From a compiled catalog of spectroscopically confirmed members, we analyze the
283 sources with reliable parallax and proper motions in the Gaia DR2 archive.
We fit the distribution of parallaxes and proper motions with multiple
populations described by multivariate Gaussians. We compute the cartesian
Galactic coordinates (X,Y,Z) and, for the populations associated with the main
cloud, also the galactic space velocity (U,V,W). We discuss the spatial
distribution of the populations in relation to the structure of the filamentary
molecular cloud traced by Herschel. Results. We discover the presence of six
populations which are all well defined in parallax and proper motions, with the
only exception being Taurus D. The derived distances range between 130 and 160
pc. We do not find a unique relation between stellar population and the
associated molecular cloud: while the stellar population seems to be on the
cloud surface, both lying at similar distances, this is not the case when the
molecular cloud is structured in filaments. Taurus B is probably moving in the
direction of Taurus A, while Taurus E appears to be moving towards them.
Conclusions. The Taurus region is the result of a complex star formation
history which most probably occurred in clumpy and filamentary structures that
are evolving independently.
