Cross-domain few-shot object detection （CD-FSOD） in aerial remote sensing aims to detect target objects when the target domain contains only a few annotated instances and differs substantially from the source domain. This setting is important for various applications （e.g.，land resource investigation，disaster monitoring，traffic supervision，maritime and airport surveillance，emergency response，and military reconnaissance），because many operational remote sensing systems must be deployed in new regions，seasons，sensors，or platforms before large-scale annotation is available. Typically，conventional object detectors assume abundant labeled data and a relatively stable training-test distribution. In contrast，aerial images are influenced by platform altitude，satellite or unmanned aerial vehicle （UAV） imaging geometry，optical or synthetic aperture radar （SAR） sensing mechanisms，spatial resolution，illumination，weather，seasonal background，geographical scene composition，and category occurrence frequency. These factors change target scale，texture，orientation，density，and contextual appearance at the same time. Consequently，detectors trained on a well-annotated source domain may suffer from severe classification confusion，localization drift，false alarms，and missed detections after being transferred to a new target domain. Related to this，the current paper provides a systematic survey of CD-FSOD for aerial remote sensing scenes. First，the task definition and research boundary are clarified. In particular，CD-FSOD is distinguished from classic object detection，few-shot object detection （FSOD），cross-domain object detection，and general remote sensing object detection. Classic object detection emphasizes classification and localization under roughly independent and identically distributed data. FSOD focuses on new-category detection with limited examples but often assumes that the base and novel domains are close. Meanwhile，cross-domain object detection addresses domain shift but usually does not impose an extreme target-domain annotation constraint. Finally，remote sensing object detection describes the application scenario and its characteristic difficulties，including small objects，dense object distributions，arbitrary orientations，and complex backgrounds. CD-FSOD integrates the last two difficulties in which the target domain is both data-scarce and distributionally shifted. Second，existing methods are organized into five technical routes. Transfer and domain-alignment methods （i.e.，domain-adaptive faster region-based convolutional neural network （DA Faster R-CNN），strong-weak distribution alignment （SWDA），spatial attention pyramid network （SAPNet），and adaptive teacher frameworks） reduce the discrepancy between source and target features by image-level，feature-level，instance-level，or teacher-student constraints. Meta-learning and metric-learning methods，including meta region-based convolutional neural network （Meta R-CNN），attention region proposal network （Attention-RPN），few-shot object detection via contrastive proposal encoding （FSCE），Detect everything with vision Transformer （DE-ViT），and CD-ViTO，all improve the use of support samples through episodic learning，class prototypes，relation modeling，and contrastive representation learning. Meanwhile，generative augmentation methods，such as hallucination-based feature synthesis，multiperspective data augmentation （MPAD），AeroGen，Control Copy-Paste，and Domain-RAG，expand the target-domain sample distribution by generating features，foreground instances，target layouts，or domain-consistent backgrounds. To compensate for insufficient visual examples，vision-language alignment methods，including RegionCLIP，PromptDet，Grounding DINO，and rich-text cross-domain multimodal FSOD，introduce category names，attributes，scene descriptions，and professional textual semantics. Furthermore，large-model methods exploit visual foundation models，detection transformer （DETR） variants，and multimodal large models （e.g.，Rex-Omni） to provide broader open-vocabulary recognition and stronger initial representations. Third，the paper summarizes datasets，task protocols，and evaluation metrics. The reviewed benchmarks include multidomain few-shot object detection （MoFSOD），CD-FSOD，object detection in optical remote sensing images （DIOR），dataset for object detection in aerial images （DOTA），xView，vehicle detection in aerial imagery （VEDAI），and the Northwestern Polytechnical University very-high-resolution 10-class dataset （NWPU VHR-10）. Their differences can be detected in terms of image number，category number，bounding-box type，scene coverage，object scale，and whether the protocol stresses a balanced K-shot instance setting. Common metrics include precision （P），recall （R），average precision （AP），mean average precision （mAP），AP50，AP75，mAP@50：95，novel-class mAP，and intersection over union （IoU）. Instead of listing formulae for routine metrics，this survey discusses their specific meanings and how they should be used to evaluate target-domain generalization，shot sensitivity，robustness across domains，and localization quality for small dense objects. Fourth，this review identifies several open problems. Notably，complex domain shift should be modeled at global-scene，local-object，and category-conditional levels rather than by a single overall feature alignment. Few-shot robustness requires support-sample quality assessment，stable prototype learning，multiscale representation，uncertainty estimation，and joint optimization of classification and localization. Current datasets and evaluation protocols remain partly disconnected from real remote sensing applications，in which categories are long-tailed，annotations are incomplete，sensors are heterogeneous，and deployment constraints are strict. To date，multisource adaptations across optical，infrared，multispectral，and SAR data remain underexplored. While foundation models and multimodal large models offer stronger semantic priors，they also introduce problems，such as high computational cost，insufficient remote sensing domain knowledge，and limited performance on small，dense，rotated，or sensor-specific targets. Therefore，to improve reuse and citation of the survey materials，a curated performance summary of representative algorithms under the aerial remote sensing CD-FSOD setting is provided in the manuscript. Overall，CD-FSOD in aerial remote sensing is moving from isolated fine-tuning or domain-alignment strategies toward integrated frameworks that combine domain adaptation，few-shot discrimination，data generation，vision-language semantics，and foundation-model transfer. In terms of practical use，it is emphasized that CD-FSOD should not be evaluated only by a single accuracy score obtained under a fixed split. Instead，a more informative protocol should report the stability of each method under different shots，target domains，object scales，and sensor conditions. This is because an algorithm that performs well on one aerial dataset may fail when the dominant background，ground sampling distance，or object density changes. Therefore，this survey recommends that future benchmark construction record the source of domain shift explicitly and separate the effects of category novelty，image style，spatial resolution，and annotation scarcity. Such analysis is especially necessary for aerial remote sensing，in which missed small targets and inaccurate localization may be more damaging than a modest decrease in overall mAP. Finally，future progress depends on remote-sensing-specific pretraining resources，reliable benchmark construction，efficient adaptation for high-resolution imagery，and stronger integration between precise detectors and general-purpose foundation models. This is maintained through the open resource page found in https://github.com/Farenweh/CD-FSOD-Links(Github) or https://gitee.com/cby1241385936/cd-fsod-links(Gitee).