Infrared small target detection is often used in different civilian and military applications to detect static or moving targets in scenes like in ground, air and sea surveillance. Research in this field started more than three decades ago, and the last two decades have witnessed very significant publications in this field following the rise of low-rank and sparse decomposition (model-based methods) and deep learning models (data-based methods). Furthermore, several surveys can be found in the literature but none of them addresses an overall review in this field. In this context, the aim of this paper is to provide a complete survey of the traditional and recent approaches in infrared small target detection. First, we categorize the different approaches found in the literature in terms of the modeling models, i.e mathematical models, machine learning models and signal processing models. Then, we have discussed them in terms of the critical situations that they claim to handle. Furthermore, we present the available resources, datasets and libraries. Then, we conclude with several promising directions for future research. For the sake of reading, this survey is divided into two parts: 1) "Traditional and Recent Approaches for Infrared Small Target Detection: Overview, Challenges and Perspectives (Part 1)" about conventional and low-rank and sparse decomposition (model-based methods), and 2) "Traditional and Recent Approaches for Infrared Small Target Detection: Overview, Challenges and Perspectives (Part 2)" about deep learning models (data-based methods).

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