Population aging increases the risk of developing neurodegenerative diseases that cause cognitive impairment. Advances in clinical practice and greater social awareness of the importance of cognitive impairment have led to an increase in the number of people with early diagnosis, predementia. Increasing access to biomarkers to assess whether Alzheimer’s disease (AD) is the underlying cause of mild cognitive impairment (MCI) has undoubted clinical benefits (access to potentially disease-modifying treatments, among others) but is also responsible for new social–health care challenges. Understanding the psychosocial impact of a diagnosis of MCI due to AD or another neurodegenerative disease is essential to create future strategies to reduce the emotional overload of patients, their risk of discrimination and stigmatization, and to favor their social inclusion. We present a narrative review of the diagnostic process of mild cognitive impairment in clinical practice, with a holistic person-centered approach, and discuss the implications of such diagnosis (benefits and risks) and strategies on how to address them.