The　arterial　pulse　wave　is　a　physiological　signal　which　can　reflect　the　function　of　the　human　cardiovascular　system.　Owing　to　the　measurement　being　convenient　and　safe,　radial　pulse　waves　have　been　often　used　in　noninvasive　monitoring　of　human　health,　which　can　further　reflect　the　health　status　of　the　cardiovascular　system,　including　information　of　the　aorta　and　peripheral　arteries.　Moreover,　radial　pulse　waves　can　assist　clinical　diagnosis　in　the　prevention　and　treatment　of　cardiovascular　disease.　This　paper　systematically　reviews　the　progress　in　analysis　of　pulse　wave　analysis,　including　pulse　wave　acquisition,　waveform　processing,　pattern　classification,　parameter　estimation,　and　clinical　applications.　In　terms　of　waveform　acquisition,　this　paper　reviews　a　variety　of　methods　to　obtain　radial　pulse　waves,　including　tonometry,　photoplethysmography,　ultrasound　manometry,　and　flexible　tactile　pressure　sensors.　In　the　aspect　of　waveform　processing,　this　paper　summarizes　the　methods　of　radial　pulse　waves　preprocessing　and　feature　extraction.　With　the　rapid　development　of　machine　learning　and　deep　learning　algorithms,　radial　pulse　waves　can　be　used　to　identify　the　status　of　human　cardiovascular　systems　and　to　estimate　parameters　related　to　cardiovascular　function.　This　paper　also　discusses　the　applications　of　radial　pulse　waves　in　clinical　practice,　including　cardiovascular　function　evaluation　and　pulse　diagnosis　in　traditional　Chinese　medicine.　Some　open-source　databases　and　analysis　software　are　also　listed.　The　current　development　trend,　challenges,　and　future　directions　of　analysis　of　radial　pulse　waves　are　also　offered.