Log-domain and translinear filters provide a competitive alternative to the challenges of ever increasing low-voltage, low-power and high frequency demands in the area of continuous-time filters. Since translinear filters are fundamentally large-signal linear, they are capable of realizing a large dynamic range in combination with excellent tunability characteristics. Large-signal linearity is achieved by exploiting the accurate exponential behavior of the bipolar transistor or the subthreshold MOS transistor. A generalization of the dynamic translinear principle exploiting the square law behavior of the MOS transistor is theoretically possible, but not practically relevant. Translinear and log-domain filters are based on the dynamic translinear principle, a generalization of the conventional (static) translinear principle. Besides their application for linear filters, dynamic translinear circuits can also be used for the realization of non-linear dynamic functions, such as oscillators, RMS-DC converters and phase-locked loops. This text covers both the analysis and synthesis of translinear circuits. The theory is presented using one unifying framework for both static and dynamic translinear networks, which is based on a current-mode approach. General analysis methods are presented, including the large-signal and non-stationary analysis of noise. A well-structured synthesis method is described greatly enhancing the designability of log-domain and translinear circuits. Comparisons are made with respect to alternative analysis and synthesis methods presented in the literature. The theory is illustrated and verified by various examples and realizations.