As Artificial Intelligence (AI) technologies continue to evolve, their use in generating realistic, contextually appropriate content has expanded into various domains. Music, an art form and medium for entertainment, deeply rooted into human culture, is seeing an increased involvement of AI into its production. However, the unregulated use of AI music generation (AIGM) tools raises concerns about potential negative impacts on the music industry, copyright and artistic integrity, underscoring the importance of effective AIGM detection. This paper provides an overview of existing AIGM detection methods. To lay a foundation to the general workings and challenges of AIGM detection, we first review general principles of AIGM, including recent advancements in deepfake audios, as well as multimodal detection techniques. We further propose a potential pathway for leveraging foundation models from audio deepfake detection to AIGM detection. Additionally, we discuss implications of these tools and propose directions for future research to address ongoing challenges in the field.