In this paper, recent results on the physics of neoclassical tearing modes (NTMs) achieved on ASDEX Upgrade are reported. A scaling law for NTM decay has been found, showing that the minimum local bootstrap current density required for mode growth is proportional to the ion gyro radius. As this scaling law does not depend on the seed island size, and thus on the background MHD activity, it is more reliable than previously derived scaling laws for the NTM onset. Furthermore, the recently reported frequently interrupted regime is discussed. In this new regime (m, n) NTMs are characterized by frequent amplitude drops caused by interaction with (m + 1, n + 1) background MHD activity. Due to the resulting reduced time averaged island size this leads to lower confinement degradation compared to that caused by the usual NTMs. As shown here, the transition into this regime can actively be triggered by lowering the magnetic shear at the q = (m + 1)/(n + 1) rational surface. Further investigations regard mechanisms to increase the,beta(N) value for NTM onset such as plasma shaping, seed island size and density profile control. Using these studies, a scenario with high beta(N) (beta(N) = 3.5) at high density (n/n(GW) = 0.83) and confinement (H-98(y,H-2) = 1.2) has been developed. Moreover, this scenario is characterized by type 11 ELM activity and thus by moderate heat load to the target plates. Finally, new NTM stabilization experiments are reported, demonstrating an increase in beta(N) after NTM stabilization.