Survival from out-of-hospital cardiac arrest depends largely on two factors: early cardiopulmonary resuscitation (CPR) and early defibrillation. CPR must be interrupted for a reliable automated rhythm analysis because chest compressions induce artifacts in the ECG. Unfortunately, interrupting CPR adversely affects survival. In the last twenty years, research has been focused on designing methods for analysis of ECG during chest compressions. Most approaches are based either on adaptive filters to remove the CPR artifact or on robust algorithms which directly diagnose the corrupted ECG. In general, all the methods report low specificity values when tested on short ECG segments, but how to evaluate the real impact on CPR delivery of continuous rhythm analysis during CPR is still unknown. Recently, researchers have proposed a new methodology to measure this impact. Moreover, new strategies for fast rhythm analysis during ventilation pauses or high-specificity algorithms have been reported. Our objective is to present a thorough review of the field as the starting point for these late developments and to underline the open questions and future lines of research to be explored in the following years.