This research paper surveys small language models (SLMs) and explores their applications, design, training, and model compression techniques. The authors explain that while large language models (LLMs) have proven effective, their resource demands have led to the development of SLMs, which are more efficient and can be deployed on a wider range of devices. The paper examines various techniques to optimize SLMs, including lightweight model architectures, efficient self-attention mechanisms, and model compression strategies such as pruning, quantization, and knowledge distillation. The authors discuss the challenges associated with SLMs, such as hallucination, bias, and energy consumption, and offer suggestions for future research. The goal of this work is to provide a comprehensive resource for researchers and practitioners working with small language models.