Natalie Wolchover of Quanta magazine recently attended the cosmology workshop at the KITP Santa Barbara, California and summarized the discussions regarding the measurement of the Hubble constant in this Quanta article.
The chart from her article (see below) shows clearly the puzzling situation. I am not an experimental (observational) cosmologist but I know that this subject is important. Keep an eye on the developments on this front.
Suresh Emre
Renaissance Universal 