  Following the intense studies on topological insulators, significant efforts
have recently been devoted to the search for gapless topological systems. These
materials not only broaden the topological classification of matter but also
provide a condensed matter realization of various relativistic particles and
phenomena previously discussed mainly in high energy physics. Weyl semimetals
host massless, chiral, low-energy excitations in the bulk electronic band
structure, whereas a symmetry protected pair of Weyl fermions gives rise to
massless Dirac fermions. We employed scanning tunneling microscopy/spectroscopy
to explore the behavior of electronic states both on the surface and in the
bulk of topological semimetal phases. By mapping the quasiparticle interference
and emerging Landau levels at high magnetic field in Dirac semimetals
Cd$_3$As$_2$ and Na$_3$Bi, we observed extended Dirac-like bulk electronic
bands. Quasiparticle interference imaged on Weyl semimetal TaAs demonstrated
the predicted momentum dependent delocalization of Fermi arc surface states in
the vicinity of the surface-projected Weyl nodes.
