  The electronic tunneling properties of the two stable forms of trilayer
graphene (TLG), rhombohedral ABC and Bernal ABA, are examined for pn and pnp
junctions as realized by using a single gate (SG) or a double gate (DG). For
the rhombohedral form, due to the chirality of the electrons, the Klein paradox
is found at normal incidence for SG devices while at high energy interband
scattering between additional propagation modes can occur. The electrons in
Bernal ABA TLG can have a monolayer- or bilayer-like character when incident on
a SG device. Using a DG however both propagation modes will couple by breaking
the mirror symmetry of the system which induces intermode scattering and
resonances that depend on the width of the DG pnp junction. For ABC TLG the DG
opens up a band gap which suppresses Klein tunneling. The DG induces also an
unexpected asymmetry in the tunneling angle for single valley electrons.
