  Transition discs are protoplanetary discs that show evidence for large holes
or wide gaps (with widths comparable to their radii) in their dust component.
These discs could be giving us clues about the disc destruction mechanism or
hints about the location and time-scales for the formation of planets. However,
at the moment there remain key gaps in our theoretical understanding. The vast
majority of transition discs are accreting onto their central stars, indicating
that - at least close to the star - dust has been depleted from the gas by a
very large amount. In this review, we discuss evidence for two distinct
populations of transition discs: mm-faint - those with low mm-fluxes, small
holes ($\lesssim$10AU) and low accretion rates (~1e-10-1e-9 Msun/yr) and
mm-bright - discs with large mm-fluxes, large holes ($\gtrsim$20 AU) and high
accretion rates ~1e-8 Msun/yr. MM-faint transition discs are consistent with
what would naively be expected from a disc undergoing dispersal; however,
mm-bright discs are not, and are likely to be rare and long-lived objects. We
discuss the two commonly proposed mechanisms for creating transition discs:
photoevaporation and planet-disc interactions, with a particular emphasis on
how they would evolve in these models, comparing these predictions to the
observed population. More theoretical work on explaining the lack of optically
thick, non-accreting transition discs is required in both the photoevaporation
and planetary hypothesis, before we can start to use transition discs to
constrain models of planet formation. Finally, we suggest that the few discs
with primordial looking SEDs, but serendipitously imaged, showing large
cavities in the mm (e.g. MWC758 & WSB 60) may represent a hidden population of
associated objects. Characterising and understanding how these objects fit into
the overall paradigm may allow us to unravel the mystery of transition discs.
