This work deals with modeling and control of thermoacoustic combustion instabilities in lean premixed combustion systems. Because of the complex interactions present in thermoacoustic systems, a network modeling approach is used. The model of each network element or subsystem is obtained analytically, numerically, or by making use of experimental techniques. The dynamics of a network system are determined experimentally by making use of a transfer matrix measurement technique. The transfer functions of a premixed flame have been determined experimentally on an atmospheric combustion test facility with a full-scale gas turbine burner, for a wide variety of operating conditions. An analytical model of the dynamic behavior of the reaction zone was made. In this model, the heat release fluctuations are assumed to be caused by fluctuations of the mass fraction of fuel and by fluctuations in the burning velocity. The model proved to be in good agreement with experimental results. Wave propagation in complex three-dimensional geometries is modeled by making use of a modal expansion technique. The modes used for the modal expansion can be obtained analytically for relatively simple geometries, or numerically (finite element method) for geometries of any complexity. By representing the modal expansion in state-space, a very numerically efficient and robust model is obtained. The thermoacoustic network model combines the state-space representations of the sub-systems in one system. The system can be analyzed in the time domain or in the frequency domain. The stability analysis is straightforward and does not require a numerical search. Non linear elements can easily be incorporated in the time domain simulation. This novel method has been validated by comparison with analytic solutions of simple thermoacoustic systems found in literature, by comparison with Finite Element codes, and by comparison with experimental results. An excellent agreement was found for all comparisons. When including non-linear elements in an annular system, a rotating acoustic field is predicted, which corresponds to experimental observations. This result has been verified analytically. Based on network models, a model based controller has been obtained using H∞ optimization. This controller has been tested in simulation and experiment on a single burner rig and proved to suppress acoustic levels by more than 25dB. An adaptive controller, based on a genetic algorithm, has been developed that does not require any knowledge about the system. This controller has been tested and proved to have similar performance as the model-based controllers. An active control system for multi-burner configurations has been developed and proved to perform well in simulations.