  ESA's INTEGRAL space mission has achieved unique results for solar and
terrestrial physics, although spacecraft operations nominally excluded the
possibility to point at the Sun or the Earth. The Earth avoidance was, however,
exceptionally relaxed for special occultation observations of the Cosmic X-ray
Background (CXB), which on some occasions allowed the detection of strong X-ray
auroral emission. In addition, the most intense solar flares can be bright
enough to be detectable from outside the field of view of the main instruments.
This article presents for the first time the auroral observations by INTEGRAL
and reviews earlier studies of the most intense solar flares. We end by briefly
summarising the studies of the Earth's radiation belts, which can be considered
as another topic of serendipitous science with INTEGRAL.
