In recent years, self-supervised learning has amassed significant interest for training deep neural representations without labeled data. One such self-supervised learning approach is masked spectrogram modeling, where the objective is to learn semantically rich contextual representations by predicting removed or hidden portions of the input audio spectrogram. With the Transformer neural architecture at its core, masked spectrogram modeling has emerged as the prominent approach for learning general purpose audio representations, a.k.a. audio foundation models. Meanwhile, addressing the issues of the Transformer architecture, in particular the underlying Scaled Dot-product Attention operation, which scales quadratically with input sequence length, has led to renewed interest in recurrent sequence modeling approaches. Among them, Selective structured state space models (such as Mamba) and extended Long Short-Term Memory (xLSTM) are the two most promising approaches which have experienced widespread adoption. While the body of work on these two topics continues to grow, there is currently a lack of an adequate overview encompassing the intersection of these topics. In this paper, we present a comprehensive overview of the aforementioned research domains, covering masked spectrogram modeling and the previously mentioned neural sequence modeling architectures, Mamba and xLSTM. Further, we compare Transformers, Mamba and xLSTM based masked spectrogram models in a unified, reproducible framework on ten diverse downstream audio classification tasks, which will help interested readers to make informed decisions regarding suitability of the evaluated approaches to adjacent applications.