In this review, from our systematic studies on transition-metal based amorphous alloys of the type (A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> ) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">75</inf> P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">16</inf> B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</inf> Al <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> , where A,B, = Fe, Ni, Mn, or Co, we demonstrate that the temperature and the field dependence of the Hall resistivity, ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</inf> , yields several useful parameters which characterize the magnetism, and the stability of these systems. The exponent for the fluctuation contribution to the magnetic susceptibility, χ, derived from these studies is found to vary from the value of 1.6, observed in general, to the Heisenberg value of 1.33 for the Fe-rich alloys. The ordinary Hall coefficient for the Ni-rich alloys is found to be negative, while a positive value is observed for all other systems studied so far. The ohmic resistivity, ρ measured simultaneously, is correlated with ρ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</inf> studies in the light of current theories. It is shown that most of the T-dependence of ρ in the metal-metalloid systems is of magnetic origin. Similar studies on the binary amorphous Zr <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">70</inf> (Fe, Co, Ni, Pd, Cu) <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">30</inf> alloys show that these systems can be understood only in terms of the extended Ziman theory. Finally, our recent evidence for deviations from the simple spin-wave theory in the magnetitions of amorphous Fe-Ni alloy system is correlated with ac-susceptibility studies to obtain a probable phase-diagram near the multicrtical point.