In this paper, we propose a synchronization and channel estimation method for amplify-and-forward two-way relay networks (AF-TWRNs) based on a low-complexity maximum-likelihood (LCML) algorithm and a joint synchronization and channel estimation (JSCE) algorithm. For synchronous AF-TWRNs, the LCML algorithm blindly estimates general nonreciprocal flat-fading channels. We formulate the channel estimation as a convex optimization problem and obtain a closed-form channel estimator. Based on the mean square error (MSE) analysis of the LCML algorithm, we propose a generalized LCML (GLCML) algorithm to perform channel estimation in the presence of the timing offset. Based on the approximation of the LCML algorithm, the JSCE algorithm is proposed to estimate jointly the timing offset and channel parameters. The theoretical analysis shows that the closed-form LCML channel estimator is consistent and unbiased. The analytical MSE expression shows that the estimation error approaches zero in scenarios with either a high signal-to-noise ratio (SNR) or a large frame length. Monte Carlo simulations are employed to verify the theoretical MSE analysis of the LCML algorithm. In the absence of perfect timing synchronization, the GLCML algorithm selects an estimation sample, which produces the optimal channel estimation, according to the MSE analysis. Simulation results also demonstrate that the JSCE algorithm is able to achieve accurate timing offset estimation.