Cross-modal content generation has become very popular in recent years. To generate high-quality and realistic content, a variety of methods have been proposed. Among these approaches, visual content generation has attracted significant attention from academia and industry due to its vast potential in various applications. This survey provides an overview of recent advances in visual content generation conditioned on other modalities, such as text, audio, speech, and music, with a focus on their key contributions to the community. In addition, we summarize the existing publicly available datasets that can be used for training and benchmarking cross-modal visual content generation models. We provide an in-depth exploration of the datasets used for audio-to-visual content generation, filling a gap in the existing literature. Various evaluation metrics are also introduced along with the datasets. Furthermore, we discuss the challenges and limitations encountered in the area, such as modality alignment and semantic coherence. Last, we outline possible future directions for synthesizing visual content from other modalities including the exploration of new modalities, and the development of multi-task multi-modal networks. This survey serves as a resource for researchers interested in quickly gaining insights into this burgeoning field.