Overall features of magnetism in amorphous transition metals have been investigated on the basis of a finite-temperature theory of the local-environment effect. It is shown that the simple ferromagnetism of Fe, Co, and Ni is drastically changed by structural disorder; amorphous transition metals form spin glasses (SG's) for compositions near amorphous Fe (6.7\ensuremath{\lesssim}N\ensuremath{\lesssim}7.35), ferromagnets for compositions near amorphous Co (7.35\ensuremath{\lesssim}N\ensuremath{\lesssim}9.0), and paramagnetisms for compositions near amorphous Ni (9.0\ensuremath{\lesssim}N\ensuremath{\lesssim}10.0) where N is the number of d electrons. The SG is accompanied by formation of local ferromagnetic clusters for N\ensuremath{\gtrsim}7.2, and shows reentrant behavior at the ferromagnetic boundary N\ensuremath{\approxeq}7.35. The ferromagnetism in amorphous transition metals is shown to be well explained by the main-peak position in the noninteracting densities of states. It is found that structural disorder enhances the Curie temperatures (${\mathit{T}}_{\mathit{C}}$) in the range 7.9\ensuremath{\lesssim}N\ensuremath{\lesssim}8.5 as compared with bcc and fcc structures. These results explain recent experimental data for the SG in Fe-rich amorphous alloys and the high ${\mathit{T}}_{\mathit{C}}$ in amorphous Co-Y alloys, but they are quite different from the early picture obtained for amorphous transition-metal--metalloid alloys.