Background: In conditions of intensive therapy, where the patients treated are in a critical condition, alarms are omnipresent. Nurses, as they spend most of their time with patients, monitoring their condition 24 h, are particularly exposed to so-called alarm fatigue. The purpose of this study is to review the literature available on the perception of clinical alarms by nursing personnel and its impact on work in the ICU environment. Methods: A systematic review of the literature was carried out according to the guidelines of the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) protocol. The content of electronic databases was searched through, i.e., PubMed, OVID, EBSCO, ProQuest Nursery, and Cochrane Library. The keywords used in the search included: “intensive care unit,” “nurse,” “alarm fatigue,” “workload,” and “clinical alarm.” The review also covered studies carried out among nurses employed at an adult intensive care unit. Finally, seven publications were taken into consideration. Data were analyzed both descriptively and quantitatively, calculating a weighted average for specific synthetized data. Results: In the analyzed studies, 389 nurses were tested, working in different intensive care units. Two studies were based on a quality model, while the other five described the problem of alarms in terms of quantity, based on the HTF (Healthcare Technology Foundation) questionnaire. Intensive care nurses think that alarms are burdensome and too frequent, interfering with caring for patients and causing reduced trust in alarm systems. They feel overburdened with an excessive amount of duties and a continuous wave of alarms. Having to operate modern equipment, which is becoming more and more advanced, takes time that nurses would prefer to dedicate to their patients. There is no clear system for managing the alarms of monitoring devices. Conclusion: Alarm fatigue may have serious consequences, both for patients and for nursing personnel. It is necessary to introduce a strategy of alarm management and for measuring the alarm fatigue level.