Most of the literature on control charts is focused on the surveillance of the mean behavior of the observed process. In our contribution we are dealing with monitoring the variance of a time series, in particular monitoring the increase of the variance. The underlying process is assumed to be a time series. In this paper we give an overview about the existing literature. In an extensive simulation study several control charts are compared with each other. The target process is assumed to be an autoregressive process of order one. In order to measure the performance of the schemes the average run length and the average delay are used. We consider charts based on the likelihood ratio approach and the generalized likelihood ratio approach, the sequential probability ratio method and the generalized sequential probability ratio procedure, the Shiryaev-Roberts procedure and a generalized Shiryaev-Roberts approach and different types of exponentially weighted moving average charts.