There is a need of continual observation of time series, with the goal of detecting an important change in the underlying process as soon as possible after it has occurred. Surveillance, statistical process control, monitoring and change-point detection are different names for this. The timeliness and also the simplicity of decisions is taken into account in the vast literature on quality control charts. Also, the literature on stopping rules is useful and relevant here. The inferential problems involved are important for the applications and interesting from a theoretical view since they are linking together different areas of statistical theory.