This book provides a framework for real time control of the Chemical Mechanical Planarization (CMP) process based on combining nonlinear dynamics principles with statistical process monitoring approaches. CMP has a direct bearing on the computational speed and dimensional characteristics of solid state devices. The challenge in CMP may be narrowed to domains enveloping productivity, measured in terms of material removal rate (MRR), and quality which is usually specified in terms of surface roughness - Ra, within wafer non-uniformity (WIWNU), defect rate, etc. In this work, experimental investigations of CMP are executed with the aid of sensors. The analysis of the data reveals the presence of pronounced stochastic-dynamic characteristics. As a result, we derive a process control method integrating statistical time series analysis and nonlinear dynamics which captures 80% (linear R-sq) of the variation in MRR. In this manner a novel paradigm for effective process control in CMP has been presented.