The degree of microphase or nanophase segregation in gradient copolymers with compositions varying across the whole copolymer backbone is studied via low-amplitude oscillatory shear (LAOS) measurements and small-angle X-ray scattering (SAXS). Studies are done as a function of comonomer segregation strength, molecular weight (MW), gradient architecture and temperature. Controlled radical polymerization is used to synthesize strongly segregating styrene/4-acetoxystyrene (S/AS) and the more weakly segregating S/n-butyl acrylate (S/nBA) gradient copolymers. Results are compared to those from S/AS and S/nBA random and block copolymers. The higher MW S/AS gradient copolymer exhibits LAOS behavior similar to the highly microphase segregated S/AS block copolymer, while the lower MW S/AS gradient copolymer exhibits complex, nonterminal behavior indicative of a lower degree of microphase segregation. The S/nBA gradient copolymers demonstrate more liquidlike behavior, with the lower MW sample exhibiting near-Newtonian behavior, indicative of a weakly segregating structure, while the higher MW, steeper gradient sample shows behavior ranging from solidlike to more liquidlike with increasing temperature. With the exception of the lower MW S/nBA case, the gradient copolymers exhibit temperature-dependent LAOS behavior over a wide temperature range, reflecting their temperature-dependent nanodomain composition amplitudes. The S/AS samples have SAXS results consistent with the degree of microphase segregation observed via rheology. Shear alignment studies are done on the higher MW S/AS gradient copolymer, which is the most highly microphase segregated gradient copolymer. Rheology and SAXS provide evidence of shear alignment, despite the gradual variation in composition profile across the nanodomains of such gradient copolymers. A short review of the nomenclature and behavior of linear copolymer architectures is also provided.