Narcolepsy type 1 (NT1) and type 2 (NT2), also known as narcolepsy with and without cataplexy, are sleep disorders that benefited from major scientific advances over the last two decades. NT1 is caused by the loss of hypothalamic neurons producing orexin/hypocretin, a neurotransmitter regulating sleep and wake, which can be measured in the cerebrospinal fluid (CSF). A low CSF level of hypocretin-1/orexin-A is a highly specific and sensitive biomarker, sufficient to diagnose NT1. Orexin-deficiency is responsible for the main NT1 symptoms: sleepiness, cataplexy, disrupted nocturnal sleep, sleep-related hallucinations, and sleep paralysis. In the absence of a lumbar puncture, the diagnosis is based on neurophysiological tests (nocturnal and diurnal) and the presence of the pathognomonic symptom cataplexy. In the revised version of the International Classification of sleep Disorders, 3rd edition (ICSD-3-TR), a sleep onset rapid eye movement sleep (REM) period (SOREMP) (i.e. rapid occurrence of REM sleep) during the previous polysomnography may replace the diurnal multiple sleep latency test, when clear-cut cataplexy is present. A nocturnal SOREMP is very specific but not sensitive enough, and the diagnosis of cataplexy is usually based on clinical interview. It is thus of crucial importance to define typical versus atypical cataplectic attacks, and a list of clinical features and related degrees of certainty is proposed in this paper (expert opinion). The time frame of at least three months of evolution of sleepiness to diagnose NT1 was removed in the ICSD-3-TR, when clear-cut cataplexy or orexin-deficiency are established. However, it was kept for NT2 diagnosis, a less well-characterized disorder with unknown clinical course and absence of biolo biomarkers; sleep deprivation, shift working and substances intake being major differential diagnoses. Treatment of narcolepsy is nowadays only symptomatic, but the upcoming arrival of non-peptide orexin receptor-2 agonists should be a revolution in the management of these rare sleep diseases.