Molecular mechanism of diseases like Alzheimer's disease (AD) and Parkinson's diseases (PD) is associated with misfolding of specific proteins, such as amyloid beta (Aβ) proteins in the case of AD, followed by their self-assembly into toxic oligomers along with the formation of amyloid fibrils assembled as plaques in the brain. Interaction of Aβ with membrane can lead to membrane damage; this process is considered as the major factor associated with the AD development. Additionally, membrane can facilitate the aggregation process of Aβ proteins. This important property of membranes is discussed in this review. A specific emphasis is given to the recently discovered property of cellular membranes to catalyze the initial step of Aβ aggregation process by which self-assembly of Aβ can be observed at physiologically low concentrations of Aβ proteins. At such low concentrations, no spontaneous aggregation occurs in the bulk solution. This fact was a major weakness of the protein aggregation model for AD. The catalytic property of membrane surfaces towards Aβ aggregation depends on the membrane composition. This finding suggests a number of novel ideas on the development of treatments and preventions for AD, which is briefly discussed in the review.