In tandem with the recent advancements in foundation model research, there has been a surge of generative music AI applications within the past few years. As the idea of AI-generated or AI-augmented music becomes more mainstream, many researchers in the music AI community may be wondering what avenues of research are left. With regards to music generative models, we outline the current areas of research with significant room for exploration. Firstly, we pose the question of foundational representation of these generative models and investigate approaches towards explainability. Next, we discuss the current state of music datasets and their limitations. We then overview different generative models, forms of evaluating these models, and their computational constraints/limitations. Subsequently, we highlight applications of these generative models towards extensions to multiple modalities and integration with artists' workflow as well as music education systems. Finally, we survey the potential copyright implications of generative music and discuss strategies for protecting the rights of musicians. While it is not meant to be exhaustive, our survey calls to attention a variety of research directions enabled by music foundation models.