  We have grown and characterized 30 nm thick YBa$_2$Cu$_3$O$_{7-\delta}$
(YBCO) films, deposited by pulsed laser deposition on both MgO (110) and
SrTiO$_3$ (001) substrates, which induce opposite strain to the superconducting
layer. By carefully tuning the in-situ post-annealing oxygen pressure, we
achieved, in a reproducible way, films at different oxygen doping, spanning
from the slightly overdoped down to the strongly underdoped region of the phase
diagram. The transport properties of the films, investigated through resistance
versus temperature measurements, are in perfect qualitative agreement with
single crystals. Starting from these films, we have also successfully
fabricated nanowires with widths down to 65 nm, at different oxygen doping. The
nanostructures exhibit characteristic temperatures (as the critical temperature
$T_{\mathrm{c}}$ and the pseudogap temperature $T^*$) similar to those of the
as-grown films and carry critical current densities $J_{\mathrm{c}}$ close to
the critical depairing value, limited by vortex entry. This implies that the
superconducting and the normal state properties of underdoped YBCO are
preserved in our films, and they can be studied as a function of the
dimensionality of the system, down to the nanoscale.
