  By scanning with a $30\, \mathrm{keV}$ focused He ion beam (He-FIB) across
YBa$_2$Cu$_3$O$_7$ (YBCO) thin film microbridges, we create Josephson barriers
with critical current density $j_\mathrm{c}$ adjustable by irradiation dose
$D$. The dependence $j_\mathrm{c} (D)$ yields an exponential decay. At $4.2\,
\mathrm{K}$, a transition from flux-flow to Josephson behavior occurs when
$j_\mathrm{c}$ decreases below $\approx 2\, \mathrm{MA/cm^2}$. The Josephson
junctions exhibit current-voltage characteristics (IVCs) that are well
described by the resistively and capacitively shunted junction model, without
excess current for characteristic voltages $V_\mathrm{c} \lesssim 1\,
\mathrm{mV}$. Devices on MgO and LSAT substrates show non-hysteretic IVCs,
while devices on SrTiO$_3$ show a small hysteresis. For all junctions an
approximate scaling $V_\mathrm{c} \propto j_\mathrm{c}^{1/2}$ is found. He-FIB
irradiation with high dose produces barriers with $j_\mathrm{c}=0$ and high
resistances of $10\, \mathrm{k\Omega} \ldots 1\, \mathrm{G\Omega}$. This
provides the possibility to write highly resistive walls or areas into YBCO
using a He-FIB. Transmission electron microscopy reveals an amorphous phase
within the walls, whereas for lower doses the YBCO stays crystalline. We have
also ``drawn'' superconducting quantum interference devices (SQUIDs) by using a
He-FIB for definition of the SQUID hole and the junctions. The SQUIDs show high
performance, with flux noise $< 500\, \mathrm{n \Phi_0/Hz^{1/2}}$ in the
thermal white noise limit for a device with $19\, \mathrm{pH}$ inductance.
