  Either in bulk form, or when exfoliated into atomically thin crystals,
layered transition metal dichalcogenides are continuously leading to the
discovery of new phenomena. The latest example is provided by 1T'-WTe$_2$, a
semimetal recently found to exhibit the largest known magnetoresistance in bulk
crystals, and predicted to become a two-dimensional topological insulator in
strained monolayers. Here, we show that reducing the thickness through facile
exfoliation provides an effective experimental knob to tune the electronic
properties of WTe$_2$, which allows us to identify the microscopic mechanisms
responsible for the observed classical and quantum magnetotransport down to the
ultimate atomic scale. We find that the longitudinal resistance and the very
unconventional B-dependence of the Hall resistance are reproduced
quantitatively in terms of a classical two-band model for crystals as thin as
six monolayers, and that for thinner crystals a crossover to an insulating,
Anderson-localized state occurs. Besides establishing the origin of the very
large magnetoresistance of bulk WTe$_2$, our results represent the first,
complete validation of the classical theory for two-band electron-hole
transport, and indicate that atomically thin WTe$_2$ layers remain gapless
semimetals, from which we conclude that searching for a topological insulating
state by straining monolayers is a challenging, but feasible experiment.
