Uncrewed Aerial Vehicle (UAV) swarms represent a transformative paradigm for scalable and resilient mission execution, yet holistic literature bridging individual dynamics and collective intelligence remains scarce. This study conducts a systematic mapping of 146 peer-reviewed articles published between 2021 and 2025, providing a broad overview of the state-of-the-art concerning the core concepts and components of a UAV swarm, progressing from individual vehicle dynamics to fully coordinated and intelligent collectives. Quantitative results reveal a dominant shift toward decentralized architectures, with connectivity maintenance and collision avoidance prioritized as the primary functional domains. Methodologically, while control theory and optimization models form the field’s "deterministic spine," data-driven AI is rapidly emerging. Despite the widespread applications of UAV swarms in simulation, the analysis exposes a significant gap in the experimental application of these, with only 19% of the reviewed research indicating hardware implementation beyond numerical simulations, identifying critical research gaps in Sim-to-Real transfer and environmental robustness. Based on the aforementioned analysis of the peer-reviewed articles, the authors propose a novel multidimensional taxonomy categorized through three lenses - coordination mechanisms, algorithmic nature, and collective behaviours - aiming to provide a structured overview of the swarming paradigms in the literature.