  Einstein's General Relativity theory has been tested in many ways during the
last hundred years as reviewed in this chapter. Two tests are discussed in
detail in this article: the concept of a zero gravity surface, the roots of
which go back to J\"arnefelt, Einstein and Straus, and the no-hair theorem of
black holes, first proposed by Israel, Carter and Hawking. The former tests the
necessity of the cosmological constant Lambda, the latter the concept of a
spinning black hole. The zero gravity surface is manifested most prominently in
the motions of dwarf galaxies around the Local Group of galaxies. The no-hair
theorem is testable for the first time in the binary black hole system OJ287.
These represent stringent tests at the limit of weak and strong gravitational
fields, respectively. In this article we discuss the current observational
situation and future possibilities.
