This is the first of two papers on Quantitative Safety Assessment – vital to the successful introduction of future Air Traffic Management systems. The goal of the two papers is to identify key future questions and the best methods to deal with them. The focus is en route European commercial traffic in controlled airspace, particularly risks from mid-air collision. Part 1 is a critical sketch of the historical context, methods used, and the use of analytical ‘models’ for safety assessment. Aspects covered include safety philosophy principles, safety targets, procedural separation standards, the Reich model and its problems, and radar separation standards.