Univariate and multivariate quality control charts are important tools for process/product monitoring and improvement. This monograph offers the developments and analyses of univariate and multivariate control charts, which are based on a generalized likelihood ratio (GLR) approach. It is commonly assumed that a process fault may shift the mean of a monitored statistic persistently to an unknown but constant value. However, there are situations such that a mean change is not constant but time varying. Incorporating a priori knowledge of a fault signature, a univariate GLR control chart is investigated for monitoring fault signatures. The GLR methodology can also be used in developing multivariate process control charts. Here, the GLR methodology is used to unify the development of various multivariate extensions to the CUSUM control charts. In addition to the GLR control charts under a normal distribution model, another GLR control chart is also proposed for monitoring a non- homogenous Markovian queuing system.