  The origin and survival of the Smith high-velocity HI cloud has so far defied
explanation. This object has several remarkable properties: (i) its prograde
orbit is ~100 km/s faster than the underlying Galactic rotation; (ii) its total
gas mass ($\gtrsim 4 \times 10^6 ~{\rm M}_{\odot}$) exceeds the mass of all
other high-velocity clouds (HVC) outside of the Magellanic Stream; (iii) its
head-tail morphology extends to the Galactic HI disc, indicating some sort of
interaction. The Smith Cloud's kinetic energy rules out models based on
ejection from the disc. We construct a dynamically self-consistent, multi-phase
model of the Galaxy with a view to exploring whether the Smith Cloud can be
understood in terms of an infalling, compact HVC that has transited the
Galactic disc. We show that while a dark-matter (DM) free HVC of sufficient
mass and density can reach the disc, it does not survive the transit. The most
important ingredient to survival during a transit is a confining DM subhalo
around the cloud; radiative gas cooling and high spatial resolution ($\lesssim$
10 pc) are also essential. In our model, the cloud develops a head-tail
morphology within ~10 Myr before and after its first disc crossing; after the
event, the tail is left behind and accretes onto the disc within ~400 Myr. In
our interpretation, the Smith Cloud corresponds to a gas 'streamer' that
detaches, falls back and fades after the DM subhalo, distorted by the disc
passage, has moved on. We conclude that subhalos with ${\rm M}_{\rm DM}
\lesssim 10^9 ~{\rm M}_{\odot}$ have accreted $\sim10^9 ~{\rm M}_{\odot}$ of
gas into the Galaxy over cosmic time - a small fraction of the total baryon
budget.
