  The Advanced LIGO and Advanced Virgo detectors have commenced observations.
Gravitational waves from the merger of binary black hole systems and a binary
neutron star system have been observed. A major goal for LIGO and Virgo is to
detect or set limits on a stochastic background of gravitational waves. A
stochastic background of gravitational waves is expected to arise from a
superposition of a large number of unresolved cosmological and/or astrophysical
sources. A cosmologically produced background would carry unique signatures
from the earliest epochs in the evolution of the Universe. Similarly, an
astrophysical background would provide information about the astrophysical
sources that generated it. The observation of gravitational waves from compact
binary mergers implies that there will be a stochastic background from these
sources that could be observed by Advanced LIGO and Advanced Virgo in the
coming years. The LIGO and Virgo search for a stochastic background should
probe interesting regions of the parameter space for numerous astrophysical and
cosmological models. Presented here is an outline of LIGO and Virgo's search
strategies for a stochastic background of gravitational waves, including the
search for gravitational wave polarizations outside of what is predicted from
general relativity. Also discussed is how global electromagnetic noise (from
the Schumann resonances) could affect this search; possible strategies to
monitor and subtract this potential source of correlated noise in a the global
detector network are explained. The results from Advanced LIGO's observing runs
O1 and O2 will be presented, along with the implications of the gravitational
wave detections. The future goals for Advanced LIGO and Advanced Virgo will be
explained.
