  We summarize the results of a dedicated effort between 2012 and 2019 to
follow the evolution of the cyclotron line in Her~X-1 through repeated NuSTAR
observations. The previously observed nearly 20-year long decay of the
cyclotron line energy has ended around 2012: from there onward the pulse phase
averaged flux corrected cyclotron line energy has remained stable and constant
at an average value of Ecyc= (37.44+/-0.07) keV (normalized to a flux level of
6.8 RXTE/ASM-cts/s). The flux dependence of Ecyc discovered in 2007 is now
measured with high precision, giving a slope of (0.675+/-0.075)
keV/(ASM-cts/s), corresponding to an increase of 6.5% of Ecyc for an increase
in flux by a factor of two. We also find that all line parameters as well as
the continuum parameters show a correlation with X-ray flux. While a
correlation between Ecyc and X-ray flux (both positive and negative) is now
known for several accreting binaries with various suggestions for the
underlying physics, the phenomenon of a long-term decay has so far only been
seen in Her~X-1 and Vela~X-1, with far less convincing explanations.
