Skin cancer persists to be one of the prevalent oncological problems worldwide and the literature has consistently held that its early-stage and accurate detection from dermoscopic images can help cure it. Over the past decade, Deep Learning (DL) paradigms have addressed this issue by replacing the conventional hand-crafted feature pipelines with networks that learn directly from the raw image pixels. This review surveyed DL approaches for dermoscopic skin cancer classification and lesion segmentation across the decade from 2016 to 2026 using the PRISMA framework. The evidence was synthesized from more than around seventy peer-reviewed studies, with a focus on the original model architectures, datasets, segmentation methods and clinical validation-based papers. The review encompasses the full arc of various DL architectures that have been applied to dermoscopy, ranging from classical convolutional neural networks (AlexNet, VGGNet, GoogLeNet, ResNet, DenseNet, EfficientNet, and MobileNet), recurrent hybrid networks (CNN-LSTM), and segmentation-first pipelines to attention mechanisms, Vision Transformers and multimodal foundation models that emerged over the years. The methods that perform both segmentation and classification were investigated in a unified manner. The key formulations behind each of the approaches are presented lucidly and the benchmarks that the field has relied upon are as follows: ISIC, HAM10000, PH2, BCN20000, Fitzpatrick17k and DDI. To ground this analysis in specific performance metrics, this review contributed cross-study plots of accuracy/AUC trajectories, accuracy-versus-model size frontiers, class imbalance issues, segmentation quality, the AI-versus-dermatologist operating space and skin-tone fairness gaps. State-of-the-art methods resulted in around 96% accuracy and an AUC approaching 0.99 on standard benchmarks; yet the issues pertaining to demographic dataset bias, opaque decision-making and unsettled regulatory norms were identified as true obstacles to trustworthy clinical deployment of DL approaches. This review concluded with a roadmap towards federated learning and multimodal, explainable and edge-deployable systems as the futuristic trends that will shape the role of AI in dermatoscopy.