The Financial Conduct Authority (FCA) wants to assess whether competition is working in the best interests of consumers, particularly in terms of them getting the best returns possible and information to meets their needs.
As well as teaser rates, where introductory deals are offered to new customers, the FCA will want to know how often consumers switch their savings accounts.
FCA chief executive Martin Wheatley said: "We know that switching rates are low for financial services products and savings accounts are no exception.
"Even when people do switch their accounts, they are twice as likely to go with their existing provider than move to the offering of a competitor."
He said the study will enable the FCA to have a better understanding of the dynamics that drive the market and the decisions that consumers make.
The review will determine whether any further action is required by the FCA.
More than 80% of adults in the UK have some kind of cash savings account, the FCA said.