Long-term survival rates are the most commonly used outcome measures for patients with cancer. However, traditional long-term survival statistics, which are derived by cohort-based types of analysis, essentially reflect the survival expectations of patients diagnosed many years ago. They are therefore often severely outdated at the time they become available. A couple of years ago, a new method of survival analysis, denoted period analysis, has been introduced to derive more 'up-to-date' estimates of long-term survival rates. We give a comprehensive review of the new methodology, its statistical background, empirical evaluation, computational realisation and applications. We conclude that period analysis is a powerful tool to provide more 'up-to-date' cancer survival rates. More widespread use by cancer registries should help to increase the use of cancer survival statistics for patients, clinicians, and public health authorities.