This paper presents a survey of retrieval algorithms used in advertising recommendation and organic content recommendation systems. Modern digital platforms rely on retrieval-based models to efficiently match users with relevant advertisements or personalized content. This survey reviews key techniques including inverted index methods, collaborative filtering, content-based filtering, hybrid recommendation models, and the two-tower neural network architecture widely used in large-scale recommendation systems. The paper compares the objectives, data utilization strategies, and evaluation metrics of ad targeting and organic retrieval systems. Practical challenges such as cold-start problems, data quality, scalability, and privacy considerations are also discussed. This survey further highlights the growing connection between industrial recommendation pipelines and emerging retrieval mechanisms used in large language model (LLM) systems. This survey provides insights into the design principles of modern retrieval systems and outlines future research directions at the intersection of recommendation systems and LLM.