Magnetic properties of Nb/Ni superconducting (SC) / ferromagnetic (FM) multilayers exhibit interesting properties near and below SC transition. A complex Field (H) – Temperature (T) phase boundary is observed in perpendicular and parallel orientation of ML with respect to DC field. We address the critical need to develop methods to make reliable magnetic measurements on SC thin films and ML, in spite of their extreme shape anisotropy and the strong diamagnetic response of the SC state. Abrupt, highly reproducible “switching” of the SC state magnetization near the normal-state FM coercive fields has been observed in Nb/Ni ML. The SC penetration depth l(Nb) > the SC coherence length xo(Nb) » 40 nm >> the FM layer thickness y(Ni) = 5 nm, abrupt magnetic reversals might be driven by strong supercurrent densities (J x M torques) that have the potential to flow into the Ni layers. Alternatively, sharp magnetization anomalies also can result from strong flux pinning by the periodic layered structure of ML, including “lock-in” of quantized flux lines (FL) parallel to the ML plane. Strong confinement of the supercurrents within ML planes might also lead to various phase transitions of the FL lattice (FLL) composed of one-dimensional chains and other unusual structures. Possible mechanisms for the switching anomalies must be evaluated while considering other experimental properties of Nb(x)/Ni(y) ML: 1) The upper critical magnetic field Hc2(T) exhibits a highly unusual anisotropy where the SC transition temperature Tc (H®0) for DC field H ^ ML plane exceeds the value for H || ML by ~ 0.5 K. 2) Nb/Ni ML samples do not consistently exhibit magnetic signatures for the onset of superconductivity, depending on the details of the sample mounting procedure and the AC or DC method used in SQUID magnetometry experiments. 3) Unusual “wiggles” or oscillations of order 10-30 mK were observed in Hc2(T) in AC SQUID experiments with H || ML and can be even larger (~0.16 K), depending upon the AC drive amplitude ho and frequency f .