Facial Expression Recognition (FER) has advanced rapidly over the last decade, driven by the shift from handcrafted descriptors and shallow classifiers to deep convolutional, attention-based, vision-language, and foundation-model architectures, and by the parallel growth of large-scale in-the-wild benchmarks spanning categorical, dimensional, compound, micro-expression, Action Unit (AU), and intensity-estimation tasks. Yet the deep learning-based FER landscape has so far been reviewed only along narrow task-, architecture-, or application-specific axes, leaving a holistic, systematically organized account of its recent advances missing. This survey addresses that gap with a comprehensive review of recent deep learning-based FER, explicitly linked to the wider Facial Affect Recognition (FAR) domain. Its main contributions are: a) A description of FER's evolution into five distinct phases, from handcrafted features and classical machine learning to attention-based, vision-language, and foundation-model approaches, with the key milestone works of each, b) A multi-criteria taxonomy analyzing the literature along seven complementary axes: recognition task, input modality, face pre-processing pipeline, network architecture, learning strategy, acquisition setting, and application domain, c) A per-criterion comparative analysis, with critical insights into the strengths and limitations of each category under in-the-wild conditions, d) A task-organized review of public FER datasets, with their annotation schemes, modalities, and evaluation protocols, e) A compilation of performance metrics and a per-task quantitative comparison of representative state-of-the-art methods on widely adopted benchmarks, and f) A discussion of current challenges and promising future directions.