Impulsive noise is a widespread and rapidly growing source of harmful interference in many applications such as vehicular communications, power line communication (PLC), underwater acoustic (UWA) communication, and Internet of Things (IoT). Noise of this type may originate from a variety of sources such as motors, high efficiency lighting, and even other wireless systems such as pulse-type or frequency-modulated continuous wave (FMCW) radars. Impulsive interference can reduce signal quality to the point of reception failure and increase bit errors resulting in degradation in system reliability. Multicarrier transmission techniques and, in particular, orthogonal frequency division multiplexing (OFDM), is proposed to cope with the frequency selectivity of the propagation channel. Although, OFDM provides some level of robustness against impulsivity by spreading the power of impulsive noise over multiple subcarriers, its performance degrades dramatically if the power of impulsive noise exceeds a certain threshold. Many mitigation techniques focus on reducing the interference before it reaches the receiver. In the context of this dissertation, the emphasis is on the reduction of interference that has already entered the signal path. Specifically, this dissertation aims to develop approaches to effectively detect and mitigate the severe impact of the impulsive noise. Here, we investigate two different categories of impulsive noise suppression techniques that can be used as a stand-alone solution or combined with other interference reduction techniques. First, we design and develop Blind Adaptive Intermittently Nonlinear Filters (BAINFs) for analog-domain mitigation of impulsive noise. The idea behind using analog domain mitigation is that insufficient processing bandwidth severely limits the effectiveness of digital nonlinear interference mitigation techniques. Therefore, the suppression of non-Gaussian noise in the analog domain before the analog to digital converter (ADC) where the outliers are more distinguishable can be helpful. The BAINFs can be implemented in many structures and we propose some sample realizations of BAINFs that can be used in different applications. In this dissertation, we consider PLC and UWA communication systems as case studies. The performance of the proposed BAINFs in these systems is quantified analytically and with experimental data. Secondly, in the classic threshold based outlier detection approaches, determining the optimum threshold is the main challenge as this threshold will vary in response to channel conditions and model mismatches. As always, there is a compromise between detection and false alarm probability in the traditional threshold based methods. To overcome this drawback, we propose a two stage impulsive noise mitigation approach. In the first stage, a machine learning approach such as a deep neural network (DNN) is used to detect the instances of impulsivity. Then, the detected impulsive noise can be mitigated in the suppression stage to alleviate the harmful effects of outliers. The robustness of the proposed DNN-based approach under (i) mismatch between impulsive noise models considered for training and testing, and (ii) bursty impulsive environment when the receiver is empowered with interleaving technique is evaluated.