  We analyzed broad-band X-ray and radio data of the magnetar SGR J1935+2154
taken in the aftermath of its 2014, 2015, and 2016 outbursts. The source soft
X-ray spectrum <10 keV is well described with a BB+PL or 2BB model during all
three outbursts. NuSTAR observations revealed a hard X-ray tail, $\Gamma=0.9$,
extending up to 79 keV, with flux larger than the one detected <10 keV. Imaging
analysis of Chandra data did not reveal small-scale extended emission around
the source. Following the outbursts, the total 0.5-10 keV flux from SGR
J1935+2154 increased in concordance to its bursting activity, with the flux at
activation onset increasing by a factor of $\sim7$ following its strongest June
2016 outburst. A Swift/XRT observation taken 1.5 days prior to the onset of
this outburst showed a flux level consistent with quiescence. We show that the
flux increase is due to the PL or hot BB component, which increased by a factor
of $25$ compared to quiescence, while the cold BB component $kT=0.47$ keV
remained more or less constant. The 2014 and 2015 outbursts decayed
quasi-exponentially with time-scales of $\sim40$ days, while the stronger May
and June 2016 outbursts showed a quick short-term decay with time-scales of
$\sim4$ days. Our Arecibo radio observations set the deepest limits on the
radio emission from a magnetar, with a maximum flux density limit of 14 $\mu$Jy
for the 4.6 GHz observations and 7 $\mu$Jy for the 1.4 GHz observations. We
discuss these results in the framework of the current magnetar theoretical
models.
