Cryptogenic infarctions are infarctions without a defined cause, despite a complete work-up. They differ from infarctions of undetermined causes, which may involve overlapping causes or an incomplete investigation. It is also different from uncommon heritable and non-heritable causes. The term embolic stroke of undetermined source (ESUS) proposed in 2014 is defined as a non-lacunar brain infarct without proximal arterial stenosis or cardioembolic sources. The major advantage of this definition compared to cryptogenic definition is the proposition of a specific work-up. In a general population, frequent potential sources of embolism in patients with ESUS have been suggested since a long time and include: patent foramen ovale (PFO), covert atrial fibrillation (AF), complex aortic arch atheroma, large vessel atheroma with stenosis<50%, carotid web, atrial cardiomyopathy, thrombophilia associated with cancer. It took almost 30 years to show, in patients under 60 with a cryptogenic stroke and a PFO, that PFO occlusion was superior to medical treatment alone for recurrent stroke. PFO under 60 is therefore no longer a cryptogenic cause of infarction. The concept of cryptogenic stroke and its refinement in ESUS have been fruitful for the identification of PFO associated as a cause. Covert AF can be detected by different techniques but its risk significance for recurrent stroke might be different from the simple electrocardiographic detection of AF. With the development of direct oral anticoagulants (DOAs), randomized studies in patients with ESUS, were run for stroke prevention but no difference was observed between patients treated by DOA compared to aspirin. These studies showed however the heterogeneity of ESUS patients. Further ESUS classification should be considered as a tool to identify homogeneous groups. We propose to further split the ESUS group into different subgroups: ESU-PFO>60-year-old, ESUS-ATH with stenosis<50%, ESUS-AF (covert AF & atrial cardiomyopathy), ESUS-cancer and others. Precision medicine is the ability to make targeted healthcare decisions based on the specific risks of individual patients. One preliminary stage is therefore to identify homogeneous groups suitable in the future for new therapeutic trials and, at the end, for new specific treatments.