AI-generated image detection technology aims to distinguish synthetic content from authentic imagery to safeguard media integrity and facilitate the subsequent forensic tasks further. In recent years，it has been a concern in the field of information security，especially in artificial intelligence-related industries such as judicial evidence verification，social media moderation，identity authentication，news broadcasting，and political security surveillance. Moreover，the growth of generative models has been promoting deep learning-based detection algorithms. In particular，the emergence of advanced techniques，such as the variational autoencoder，generative adversarial network，and denoising diffusion probabilistic model，has led to a qualitative leap in synthesis quality. However，a comprehensive review and analysis of state-of-the-art deep learning-based detection algorithms for different generative attacks are required to be realized to address the current theoretical fragmentation. Thus，we develop a systematic and critical review to explore the developments of AI-generated image detection in recent years. First，a comprehensive and systematic introduction of the detection field is presented from the following three aspects： 1） the evolution of forensic technology from handcrafted features to deep representations，2） the prevailing deepfake datasets，and 3） the common evaluation metrics. Then，more extensive qualitative experiments，quantitative experiments，and generalization evaluations of representative detection methods are conducted on the public datasets to compare their performance. Finally，the summary and challenges in the forensic community are highlighted. In particular，some prospects are recommended further in the field of digital forensics. First，from the perspective of learning paradigms，the existing image detection methods can be divided into two fundamental categories，i.e.，the disproof paradigm aimed at identifying falsity，and the truth-preserving paradigm aimed at modeling reality. Specifically，the disproof paradigm focuses on extracting specific forgery traces including frequency domain artifacts and spatial inconsistencies，while the truth-preserving paradigm targets the modeling of intrinsic real image distributions to detect anomalies. In addition，the domain of deep learning-based detection algorithms can be classified into the convolutional neural network-based fusion framework and vision transformer-based framework from the aspect of network architectures. The disproof-based framework achieves the feature extraction of manipulation signatures by supervised binary classification and accomplishes deep feature discrimination via learning distinguishable boundaries between real and fake domains. To clarify the transition of methodologies，the truth-preserving framework is originated from one-class classification and reconstruction principles. From the perspective of the supervision paradigm，the deep learning detection methods can also be categorized into three classes，i.e.，supervised learning，unsupervised learning，and self-supervised learning. The supervised methods leverage labeled synthetic data to guide the training processes，and the unsupervised approaches construct loss functions via constraining the similarity between the input and the learned manifold of natural images. The self-supervised algorithms are associated with the masked image modeling framework in common. Our critical review is focused on the main concepts and discussions of the characteristics of each method for different forensic scenarios from the perspectives of the network architecture and learning paradigm. First，we summarize the limitations of different algorithms，such as the generalization failure of disproof methods and the modeling complexity of truth-preserving methods，and provide some recommendations for further research. Second，we briefly introduce the popular public datasets such as FaceForensics++ and Wilddeepfake and provide the interfaces related to download them for each specific detection scenario. Then，we present the common evaluation metrics in the forensic field from two aspects： classification-based evaluation metrics and robustness-based metrics designed for cross-generator settings. The generic metrics can be utilized to evaluate the precision and sensitivity of algorithms of those are accuracy-based，error rate-based，receiver operating characteristic-based，and area under the curve-based metrics in total. Some of the generic metrics，such as accuracy （ACC），area under the curve （AUC），equal error rate （EER），and true positive rate （TPR），are also used for the quantitative assessment of generalization. The specific metrics designed for localization consist of pixel-level intersection over union and bounding box precision that employ the pixel-wise masks as the reference ground truth. Third，we present the qualitative and quantitative results，and average inference times of representative alternatives for various forensic missions. Finally，this review critically analyzes the conclusion，highlights the challenges in the detection community，and conducts forecasting analysis，such as cross-domain image detection，high-level semantic consistency-driven detection，antiforensic robust detection，real-time mobile detection，explainable forensics based on physical imaging principles，detection under extreme compression，and comprehensive evaluation benchmarks. The methods，datasets，and evaluation metrics mentioned are linked at https://github.com/qqqqwddw/wesome-image-Detection and https://www.scidb.cn/detail?dataSetId=d6427185d9ff4c43bb6b190a117d723b.