In this talk, we explore Linearized Reactive Field (LRF) methods and their developing role in comprehending the dynamics of turbulent combustion. We will begin with a brief overview of linearized mean field methods, highlighting their significance in revealing the importance of coherent structures in turbulent flows. We will explore key theoretical concepts integral to our approach, such as triple decomposition, linear stability, and resolvent analysis. To begin, we will examine nonreacting flows, using amplifier and oscillator flows as examples. From there, we will move on to reacting flows, where we will introduce fundamental equations and address the multi-closure problem, a major hurdle in the modelling of combustion dynamics. Emphasis will be placed on the innovative approach of data assimilation as a means of effectively addressing this closure problem. We detail the suite of tools developed for studying LRF methods to facilitate their implementation and comprehension. These tools incorporate various techniques, such as combustion experiments, Large Eddy Simulations, Physics-Informed Neural Networks, and the Finite Element Linearized Reacting Field Solver (FELICS). The presentation will illustrate multiple examples of LRF techniques in the field of combustion dynamics, which tackle the propagation of entropy and swirl fluctuations, as well as turbulent flow-flame interactions. To summarise, a future outlook will be provided on LRF application, with a particular focus on the transition to hydrogen combustion.