In recent years several studies have been conducted to establish a theoretical basis for the performance of molecular communication networks. The general aim of this thesis is to study the performance of diffusion-based molecular communication networks that use molecular circuits (i.e. a set of chemical reactions) at the transmitter or receiver, from a communication theory perspective. First we consider a diffusion-based molecular communication system where the transmitter uses Reaction Shift Keying (RSK) as the modulation scheme. We focus on the demodulation of RSK signals at the receiver, which consists of a front-end molecular circuit and a back-end demodulator. The optimal demodulator computes the posteriori probability of the transmitted symbols given the history of the observation. The derivation of the optimal demodulator requires the solution to a specific Bayesian filtering problem. Our key contribution is to present a general solution to this Bayesian filtering problem which can be applied to any molecular circuit and any choice of observed species. We present a few examples where we have applied this generalised solution to different receiver molecular circuits. We show that enzymatic reaction cycles (ERCs), a class of chemical reactions commonly found in cells and consisting of a forward and a backward enzymatic reaction, can improve the capacity of a molecular communication link. The technical difficulty in analysing ERCs is the nonlinear reaction rates. We deal with this by assuming that the amount of certain chemicals in the ERCs is large. To further simplify the problem, we use singular perturbation to study a particular operating regime of the ERCs. This allows us to derive a closed-form expression of the channel gain which suggests that channel gain can be improved by increasing the total amount of substrate in the ERCs. By using numerical calculations, we show that the effect of the ERCs is to increase the channel gain and to reduce the noise, which results in a better signal to noise ratio and in turn a higher communication capacity. Finally, we present a diffusion-based molecular communication system where both the transmitter and receiver are based on molecular circuits. By matching different transmitter and receiver circuit pairs we determine which combination of reactions at the transmitter and receiver yield better communication performance.