  Magnetoresistance (MR) is a characteristic that the resistance of a substance
changes with the external magnetic field, reflecting various physical origins
and microstructures of the substance. A large MR, namely a huge response to a
low external field, has always been a useful functional feature in industrial
technology and a core goal pursued by physicists and materials scientists.
Conventional large MR materials are mainly manganites, whose colossal MR (CMR)
can be as high as -90%. The dominant mechanism is attributed to spin
configuration aligned by the external field, which reduces magnetic scattering
and thus resistance. In recent years, some new systems have shown an extremely
large unsaturated MR (XMR). Unlike ordinary metals, the positive MR of these
systems can reach 103-108% and is persistent under super high magnetic fields.
The XMR materials are mainly metals or semimetals, distributed in high-mobility
topological or non-topological systems, and some are magnetic, which suggests a
wide range of application scenarios. Various mechanisms have been proposed for
the potential physical origin of XMR, including electron-hole compensation,
steep band, ultrahigh mobility, high residual resistance ratio, topological
fermions, etc. It turns out that some mechanisms play a leading role in certain
systems, while more are far from clearly defined. In addition, the researches
on XMR are largely overlapped or closely correlated with other recently rising
physics and materials researches, such as topological matters and
two-dimensional (2D) materials, which makes elucidating the mechanism of XMR
even more important. Moreover, the disclosed novel properties will lay a broad
and solid foundation for the design and development of functional devices. In
this review, we will discuss several aspects in the following order: ...
