Reaction network theories are tools for stability analysis of open reacting systems provided that stoichiometric (chemical) equations are given for each reaction step together with power law rate expressions. Based on stoichiometry alone, elementary subnetworks (known also as elementary modes or extreme currents) are identified and their capacity for displaying dynamical instabilities, such as bistability and oscillations, is evaluated by examining associated Jacobian matrix. This analysis is qualitative in the sense that only reaction orders are needed as input information, whereas rate coefficients may remain unspecified. In the next step, the subnetworks are combined to form the entire network and its stability is determined by stability of the constituting subnetworks. This combination principle can be conveniently used for kinetic parameter estimation of the unknown/unspecified rate coefficients by applying linear optimization to a set of constraint equations balancing linearly combined subnetworks with the corresponding rate expressions. Mathematically, this amounts to convex optimization. From the application point of view, we wish to describe an experimentally measured biosystem in which chemical processes take place (such as enzyme control loops, metabolism, gene regulation, etc.) giving rise to experimentally observed change from a steady state to oscillatory or bistable dynamics. For such a system a reaction mechanism is assumed (or available from previous research) with only a limited set of known kinetic parameters, in addition to input/output parameters known from the experiment. Then the set of unknown kinetic parameters is estimated via linear optimization so that the dynamics displayed by the model coincides with the experimentally observed behavior (emergence of oscillations or bistable switch). Such an estimate may not yield the ultimate best fit, rather, it helps to locate a region in the parameter space, where the observed dynamics are reproduced by the model. This global approach is useful especially when the number of unknown parameters is large. Once a suitable parameter region is found, standard least-square methods or other more refined algorithms assuming a well chosen initial guess may be used to fine tune the parameters values. In addition, reaction network theory is useful in identifying subnetworks that are responsible for destabilizing the steady state. In particular, such subnetworks provide prototypes of chemical oscillators, also called oscillatory motifs, which possess a characteristic network topology. Thus the search for dynamical instabilities in arbitrarily large networks, as is typical in biosystems, can be reduced to the search for motifs.