Cloud environments compose unique operational characteristics and intrinsic capabilities such as service transparency and elasticity. By virtue of their exclusive properties as being outcomes of their virtualized nature, these environments are prone to a number of security threats either from malicious or legitimate intent. By virtue of the minimal proactive properties attained by off-the-shelf signature-based commercial detection solutions employed in various infrastructures, cloud-specific Intrusion Detection System (IDS) Anomaly Detection (AD)-based methodologies have been proposed in order to enable accurate identification, detection, and clustering of anomalous events that could manifest. Therefore, in this chapter the authors firstly aim to provide an overview in the state of the art related with cloud-based AD mechanisms and pinpoint their basic functionalities. They subsequently provide an insight and report some results derived by a particular methodology that jointly considers cloud-specific properties and relies on the Empirical Mode Decomposition (EMD) algorithm.