Alzheimer's disease (AD) is the most common cause of dementia, affecting 35 million people worldwide. One pathological feature of progressing AD is the loss of synapses. This is the strongest correlate of cognitive decline. Astrocytes, as an essential part of the tripartite synapse, play a role in synapse formation, maintenance, and elimination. During AD, astrocytes get a reactive phenotype with an altered gene expression profile and changed function compared to healthy astrocytes. This process likely affects their interaction with synapses. This systematic review aims to provide an overview of the scientific literature including information on how astrocytes affect synapse formation and elimination in the brain of AD patients and in animal models of the disease. We review molecular and cellular changes in AD astrocytes and conclude that these predominantly result in lower synapse numbers, indicative of decreased synapse support or even synaptotoxicity, or increased elimination, resulting in synapse loss, and consequential cognitive decline, as associated with AD. Preventing AD induced changes in astrocytes might therefore be a potential therapeutic target for dementia.