In many practical applications, it is well known that data collected inevitably contain one or more anomalous outliers; that is, observations that are well separated from the majority or bulk of the data, or in some fashion deviate from the general pattern of the data. The occurrence of outliers may be due to misplaced decimal points, recording errors, transmission errors, or equipment failure. These outliers can lead to erroneous parameter estimation and consequently affect the correctness and accuracy of the model inference. In order to solve these problems, three robust fuzzy neural networks (FNNs) will be proposed in this dissertation. This provides alternative learning machines when faced with general nonlinear learning problems. Our emphasis will be put particularly on the robustness of these learning machines against outliers. Though we consider only FNNs in this study, the extension of our approach to other neural networks, such as artificial neural networks and radial basis function networks, is straightforward. In the first part of the dissertation, M-estimators, where M stands for maximum likelihood, frequently used in robust regression for linear parametric regression problems will be generalized to nonparametric Maximum Likelihood Fuzzy Neural Networks (MFNNs) for nonlinear regression problems. Simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) will be derived. In the second part of the dissertation, least trimmed squares estimators, abbreviated as LTS-estimators, frequently used in robust (or resistant) regression for linear parametric regression problems will be generalized to nonparametric least trimmed squares fuzzy neural networks, abbreviated as LTS-FNNs, for nonlinear regression problems. Again, simple weight updating rules based on gradient descent and iteratively reweighted least squares (IRLS) algorithms will be provided. In the last part of the dissertation, by combining the easy interpretability of the parametric models and the flexibility of the nonparametric models, semiparametric fuzzy neural networks (semiparametric FNNs) and semiparametric Wilcoxon fuzzy neural networks (semiparametric WFNNs) will be proposed. The corresponding learning rules are based on the backfitting procedure which is frequently used in semiparametric regression.