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This paper reviews concepts, modeling approaches, and recent findings along a spectrum of different levels of abstraction of neural network models including generalization across (1) Samples, (2) Distributions, (3) Domains, (4) Tasks, (5) Modalities, and (6) Scopes. Strategies for (1) sample generalization from training to test data are discussed, with suggestive evidence presented that, at least for the ImageNet dataset, popular classification models show substantial overfitting. An empirical example and perspectives from statistics highlight how models' (2) distribution generalization can benefit from consideration of causal relationships and counterfactual scenarios. Transfer learning approaches and results for (3) domain generalization are summarized, as is the wealth of domain generalization benchmark datasets available. Recent breakthroughs surveyed in (4) task generalization include few-shot meta-learning approaches and the emergence of transformer-based foundation models such as those used for language processing. Studies performing (5) modality generalization are reviewed, including those that integrate image and text data and that apply a biologically-inspired network across olfactory, visual, and auditory modalities. Higher-level (6) scope generalization results are surveyed, including graph-based approaches to represent symbolic knowledge in networks and attribution strategies for improving networks' explainability. Additionally, concepts from neuroscience are discussed on the modular architecture of brains and the steps by which dopamine-driven conditioning leads to abstract thinking.