The use of standard and reliable measurements is essential in many areas of life, but nowhere is it of more crucial importance than in the world of science, and physics in particular. This book contains 20 contributions presented as part of Course 206 of the International School of Physics Enrico Fermi on New Frontiers for Metrology: From Biology and Chemistry to Quantum and Data Science, held in Varenna, Italy, from 4 -13 July 2019. The Course was the 7th in the Enrico Fermi series devoted to metrology, and followed a milestone in the history of measurement: the adoption of new definitions for the base units of the SI. During the Course, participants reviewed the decision and discussed how the new foundation for metrology is opening new possibilities for physics, with several of the lecturers reflecting on the implications for an easier exploration of the unification of quantum mechanics and gravity. A wide range of other topics were covered, from measuring color and appearance to atomic weights and radiation, and including the application of metrological principles to the management and interpretation of very large sets of scientific data and the application of metrology to biology. The book also contains a selection of posters from the best of those presented by students at the Course. Offering a fascinating exploration of the latest thinking on the subject of metrology, this book will be of interest to researchers and practitioners from many fields.