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Purpose: Artifacts in magnetic resonance imaging (MRI) scans degrade image quality and thus negatively affect the outcome measures of clinical and research scanning. Considering the time-consuming and subjective nature of visual quality control (QC), multiple (semi-)automatic QC algorithms have been developed. This systematic review presents an overview of the available (semi-)automatic QC algorithms and software packages designed for raw, structural T1-weighted (T1w) MRI datasets. The objective of this review was to identify the differences among these algorithms in terms of their features of interest, performance, and benchmarks. Methods: We queried PubMed, EMBASE (Ovid), and Web of Science databases on the fifth of January 2023, and cross-checked reference lists of retrieved papers. Bias assessment was performed using PROBAST (Prediction model Risk Of Bias ASsessment Tool). Results: A total of 18 distinct algorithms were identified, demonstrating significant variations in methods, features, datasets, and benchmarks. The algorithms were categorized into rule-based, classical machine learning-based, and deep learning-based approaches. Numerous unique features were defined, which can be roughly divided into features capturing entropy, contrast, and normative measures. Conclusion: Due to dataset-specific optimization, it is challenging to draw broad conclusions about comparative performance. Additionally, large variations exist in the used datasets and benchmarks, further hindering direct algorithm comparison. The findings emphasize the need for standardization and comparative studies for advancing QC in MR imaging. Efforts should focus on identifying a dataset-independent measure as well as algorithm-independent methods for assessing the relative performance of different approaches. [ABSTRACT FROM AUTHOR]