Sleep plays a fundamental role in the lives of many animals, from some invertebrates to humans. It has both physiological and behavioral connotations and, although its functions and evolutionary significance are not yet fully known, its fundamental role in the maintenance of homeostasis and the adverse effects due to its sub-optimality are well-known in humans. Indeed, it influences attention, memory, mood, blood pressure, immune and inflammatory response, and stress response ^[1][2][3][1,2,3]. Under physiological conditions, a sleep phase and a wakefulness phase alternate in a regular manner, constituting the sleep–wake circadian rhythm. The sleep phase is a dynamic process aimed at obtaining the required neurophysiological states at certain times, according to circadian and homeostatic needs and despite external or internal interfering stimuli. Moreover, the so-called macrostructure of sleep, as recorded by electroencephalography (EEG) during polysomnography (PSG), is characterized by a chain of regular and predictable events (cyclic alternation of rapid eye movements (REM) and non-REM (NREM) sleep stages). The process shows an intrinsic variability and has to finely modulate itself in order to maintain the maximum adaptability while preserving sleep macrostructure. In this context, peculiar transient EEG patterns (sleep microstructure) are supposed to play the main role in the building up of EEG synchronization and in the flexible adaptation against perturbations. Alterations in sleep macro- or microstructure provoke sleep disruption, sleep instability and loss of sleep quantity and quality ^[4][5][4,5]. Sleep and wakefulness influence each other; therefore, sleep quality degradation, when persisting over time, may translate into severe and irreversible symptoms, taking the form of a pathological framework. Therefore, it is very important to create the best possible sleeping conditions and to intervene promptly when sleep disturbances occur, both in their diagnosis and eventual treatments. Even though sleep time and quality lessen with age, sleep disorders are related to comorbidities rather than age [6]. In particular, sleep disorders have a high incidence in neurodegenerative diseases (ND) and are known to influence well-being and quality of life [7]. Indeed, the symptoms of the NDs may be worsened by the sleep disorders, but, at the same time, the latter may be caused or augmented by the neurodegenerative disease, creating a more complex clinical picture. Optimized, sometimes individualized, treatments are being developed in clinical practice [8]. The relationship between sleep abnormalities/disorders and NDs is so close that sleep disorders can be used as criteria for the diagnosis of specific NDs [9]. As an example, stridor co-occurs with multiple system atrophy (MSA), while a REM-sleep behavior disorder may discriminate between Alzheimer’s disease (AD) and dementia with Lewy body (DLB). The most interesting discovery in the field is that, in some cases, especially in Parkinson’s disease (PD), the onset of sleep disturbance could reflect early alterations in the neural pathways involved, thus constituting a prodromal symptom [10]. This allows earlier intervention in treatment and follow-up; moreover, it will be crucial when neuroprotective drugs become available [11]. The assessment of sleep macro- and microstructure, movements, respiratory pattern or other neurophysiological changes that occur during sleep is essential to verify the quality of sleep and detect sleep disorders. For clinical purposes, PSG is the gold standard for the assessment of sleep disorders, and guidelines are available for recommended uses. In PSG, selected electrophysiological signals are recorded along with other biological signals of interest, such as airflow, oxygen saturation, chest movements or snoring. The type and number of signals that are recorded depends on the reported symptoms and the aim of the PSG. EEG, electrooculography (EOG), electrocardiography (ECG), and electromyography (EMG) are required for sleep staging, whereas in the detection of sleep apnea, for instance, the primary focus is on oxygen saturation, airflow, and thorax and abdominal movements [12]. Complete polysomnographic examinations are very complex and invasive; they need cumbersome instrumentation, a proper location, night-time assistance by experienced personnel, time, money and they bring discomfort for the patient as well. The medical inspection of the signals (many hours of recording) needs to be performed by qualified experts and it is, however, subjected to inter- operator variability ^[13][14][13,14]. For these reasons, PSG can only be performed in proper settings and usually for in-patients, mainly when precise diagnosis is essential for targeting therapy. Therefore, many alternatives have been proposed in the research to cope with this limitation, in particular for screening or monitoring purposes. They exploit, in general, new technologies and automatic algorithms to reduce the invasiveness of the instrumentation required and the intervention of specialized personnel. This would allow a much more frequent, if not continuous, assessment of the patients’ condition with reduced cost and discomfort, providing the conditions for optimized diagnosis and treatments. Research in this area has several objectives:

• To update and simplify the work of medical staff by automating or semi-automating certain procedures—such as sleep staging or sleep disorders diagnosis—through new instrumentation.