  RX J0806.3+1527 is thought to be a 321s orbital period (the shortest known)
double white dwarf binary system. According to the double degenerate binary
(DDB) scenario this source is expected to be one of the strongest gravitational
wave (GW) emitter candidates. In the last years RX J0806.3+1527 has been
studied in great details, through multiwavelength observational campaigns and
from the point of view of data analysis result interpretations. We present here
the timing results obtained thanks to a 3.5-year long optical monitoring
campaign carried out by the Very Large Telescope (VLT) and the Telescopio
Nazionale Galileo (TNG) which allowed us to detect and study the orbital period
derivative (spin-up at a rate of about 10^-3 s/yr) of the 321s modulation, to
detect the linear polarisation (at a level of about 2%), and to study the broad
band energy spectrum. The VLT/TNG observational strategy we used allowed us to
rely upon a P-Pdot coherent solution which we finally extended backward to the
1994 ROSAT observation of RX J0806.3+1527.
