This paper aims to summarize and map contemporary views on some contentious aspects of arterial hemodynamics that have remained unresolved despite years of research. These were discussed during a workshop entitled Arterial hemodynamics: past, present and future held in London on June 14 and 15, 2016. To do this we formulated a list of potential consensus statements informed by discussion at the meeting in London and quantified the degree of agreement and invited comments from the participants of the workshop. Overall the responses and comments show a high measure of quantitative agreement with the various proposed ‘consensus’ statements. Taken together, these statements seem a useful basis for proceeding with a more detailed and comprehensive consensus document on the current understanding and approaches to analysis of the pulse waveform. Future efforts should be directed at identifying remaining areas of dispute and future topics for research.