Advanced scenarios in tokamaks seek to maximize the confinement and stability of thermonuclear plasmas. Key to obtaining these conditions is operation at different current density profiles. Experiments at ASDEX Upgrade are reported with approximately zero magnetic shear in the center or reversed magnetic shear in the center. With zero magnetic shear and q0 near 1, stationary conditions are obtained in discharges without sawteeth at 800 kA and 1 MA and q95 = 3.3 to 4.5, using a combination of central neutral beam injection (NBI) heating and off-axis NBI heating. In this regime, the temperature profiles are stiff. Central heating with ion cyclotron resonance heating and electron cyclotron resonance heating can be used to prevent excessive density peaking to maximize the stability against neoclassical tearing modes and to prevent impurity accumulation. At a lower plasma current of 400 kA with 10 MW of NBI heating, the bootstrap current fraction in this regime is above 50% giving, with the NBI current drive, nearly fully noninductively driven conditions. Operation at average electron densities of 80 to 90% of the Greenwald density limit is obtained at a triangularity of = 0.43 achieving N = 3.5 in stationary conditions. Moreover, in these plasmas, type II edge-localized modes are observed in configurations close to double null. In plasmas with a reversed magnetic shear in the center, the formation of ion transport barriers with NBI heating was optimized to obtain more reproducible transport barriers with an H-mode edge for maximum stability, achieving, transiently, N values of 4. With a 1.6 MW counter electron cyclotron current drive in the center and densities in the range <ne> = 1.3 to 2.0 × 1019 m-3, a reversed magnetic shear and electron internal transport barriers are formed and sustained at 600 kA for 1 to 2 s with Te0 > 20 keV. Of the scenarios presented, the stationary plasmas with low magnetic shear in the center and q95 in the range 3.3 to 4.5 would obtain reactor-relevant values for H × N/q952, a figure of merit used as a benchmark.