The escalating carbon footprint of artificial intelligence (AI) models presents a significant environmental concern, primarily because of the increasing need for large-scale and computationally intensive systems. Therefore, based on efforts to minimize the carbon footprint of AI models, this paper reviews key strategies within the emerging field of Green AI, which aims to reduce AI's environmental impacts by enhancing efficiency and sustainability. First, the paper contextualizes the problem by highlighting the substantial energy demands and carbon emissions linked to the training and deployment of AI models, including the often-overlooked influence of the model's programming language choice, as a single AI model could generate over 284 tonnes of CO₂ over 6 months. Since algorithmic optimization contributes directly to reducing the AI model's carbon footprint, it is therefore, in this paper we delve into algorithmic optimization techniques, with a particular focus on model compression as a crucial approach to reducing AI's energy footprint, as this review provides a thorough overview of the primary model compression methodologies: pruning, quantization, and knowledge distillation, detailing their types, mechanisms, and documented benefits in achieving significant energy savings and enabling deployment on resource-constrained devices(e.g. knowledge distillation, as a model compression contributed to minimizing energy use by as much as 184 times and carbon emissions by up to 157 times). Finally, the review discusses essential Green AI benchmarking metrics, encompassing both traditional AI performance indicators and novel energy consumption and carbon emission measurements. We also explore practical software-based and hardware-accurate tools available to programmers for quantifying the environmental implications of their AI development workflows.