Large, multi-site, heterogeneous brain imaging datasets are increasingly required for the training, validation, and testing of advanced deep learning (DL)-based automated tools, including structural magnetic resonance (MR) image-based diagnostic and treatment monitoring approaches. When assembling a number of smaller datasets to form a larger dataset, understanding the underlying variability between different acquisition and processing protocols across the aggregated dataset (termed “batch effects”) is critical. The presence of variation in the training dataset is important as it more closely reflects the true underlying data distribution and, thus, may enhance the overall generalizability of the tool. However, the impact of batch effects must be carefully evaluated in order to avoid undesirable effects that, for example, may reduce performance measures. Batch effects can result from many sources, including differences in acquisition equipment, imaging technique and parameters, as well as applied processing methodologies. Their impact, both beneficial and adversarial, must be considered when developing tools to ensure that their outputs are related to the proposed clinical or research question (i.e., actual disease-related or pathological changes) and are not simply due to the peculiarities of underlying batch effects in the aggregated dataset. We reviewed applications of DL in structural brain MR imaging that aggregated images from neuroimaging datasets, typically acquired at multiple sites. We examined datasets containing both healthy control participants and patients that were acquired using varying acquisition protocols. First, we discussed issues around Data Access and enumerated the key characteristics of some commonly used publicly available brain datasets. Then we reviewed methods for correcting batch effects by exploring the two main classes of approaches: Data Harmonization that uses data standardization, quality control protocols or other similar algorithms and procedures to explicitly understand and minimize unwanted batch effects; and Domain Adaptation that develops DL tools that implicitly handle the batch effects by using approaches to achieve reliable and robust results. In this narrative review, we highlighted the advantages and disadvantages of both classes of DL approaches, and described key challenges to be addressed in future studies.