This article presents a survey of cellular network sharing, which is a key building block for virtualizing future mobile carrier networks in order to address the explosive capacity demand of mobile traffic, and reduce the CAPEX and OPEX burden faced by operators to handle this demand. We start by reviewing the 3GPP network sharing standardized functionality followed by a discussion on emerging business models calling for additional features. Then an overview of the RAN sharing enhancements currently being considered by the 3GPP RSE Study Item is presented. Based on the developing network sharing needs, a summary of the state of the art of mobile carrier network virtualization is provided, encompassing RAN sharing as well as a higher level of base station programmability and customization for the sharing entities. As an example of RAN virtualization techniques feasibility, a solution based on spectrum sharing is presented: the network virtualization substrate (NVS), which can be natively implemented in base stations. NVS performance is evaluated in an LTE network by means of simulation, showing that it can meet the needs of future virtualized mobile carrier networks in terms of isolation, utilization, and customization.