  The introduction of topological invariants, ranging from insulators to
metals, has provided new insights into the traditional classification of
electronic states in condensed matter physics. A sudden change in the
topological invariant at the boundary of a topological nontrivial system leads
to the formation of exotic surface states that are dramatically different from
its bulk. In recent years, significant advancements in the exploration of the
physical properties of these topological systems and regarding device research
related to spintronics and quantum computation have been made. Here, we review
the progress of the characterization and manipulation of topological phases
from the electron transport perspective and also the intriguing chiral/Majorana
states that stem from them. We then discuss the future directions of research
into these topological states and their potential applications.
