The increasing share of renewables creates new challenges for the existing electrical grid. To deal with these challenges, various efforts are being made to transform the existing power grid into a so-called smart grid. Part of this process is the deployment of an advanced metering infrastructure, which provides novel high-frequency two-way communication between consumers and producers. But as useful as the access to high-frequency measurements may be for energy suppliers, this also poses a major threat to the privacy of the customers. In this survey we present approaches to the problem of customer privacy-protection in the smart grid. We show that the privacy problem in smart grids can be further divided into the problems metering for billing and metering for operations. For each of these problems we identify generic approaches to solve them.