Real-time condition monitoring of complex dynamical systems is of critical importance for predictive maintenance. This chapter focuses on data-driven techniques of fault diagnostics with an emphasis on real-time detection of anomalous behavior in combustion systems. It presents the applications of well-known statistical learning techniques such as D-Markov modeling and hidden Markov modeling (HMM) as possible data-driven solutions for anomaly detection in combustion systems. From the perspective of real-time monitoring and diagnostics, such statistical tools are applicable to stochastic dynamical systems in general. Both D-Markov and HMM algorithms have been validated on experimental data from a laboratory apparatus, which is an electrically heated Rijke tube.