Our galaxy contains a great number of stellar mass compact objects which are generally thought to be black holes. Precise x-ray observations of a thermal spectrum of the accretion disk can be used to determine whether or not these objects are in fact the black holes predicted by general relativity. The Kerr metric is completely specified by two parameters: the mass, M, and the spin, J, of the compact object. All the terms in the multipole moment expansion of the gravitational field can be immediately deduced from these two quantities; thus the determination of the quadrupole moment can be used to test the Kerr nature of astrophysical black hole candidates. In this talk, I will discuss theoretical studies that allow current observational data of the X-ray spectrum of stellar-mass black hole candidates to already put interesting constraints on the interpretation of these objects.