Multimodal Generative Models (MGMs) have rapidly evolved beyond text generation, now spanning diverse output modalities including images, music, video, human motion, and 3D objects, by integrating language with other sensory modalities under unified architectures. This survey categorises six primary generative modalities and examines how foundational techniques, namely Self-Supervised Learning (SSL), Mixture of Experts (MoE), Reinforcement Learning from Human Feedback (RLHF), and Chain-of-Thought (CoT) prompting, enable cross-modal capabilities. We analyze key models, architectural trends, and emergent cross-modal synergies, while highlighting transferable techniques and unresolved challenges. Building on a common taxonomy of models and training recipes, we propose a unified evaluation framework centred on faithfulness, compositionality, and robustness, and synthesise evidence from benchmarks and human studies across modalities. We further analyse trustworthiness, safety, and ethical risks, including multimodal bias, privacy leakage, and the misuse of high-fidelity media generation for deepfakes, disinformation, and copyright infringement in music and 3D assets, together with emerging mitigation strategies. Finally, we discuss how architectural trends, evaluation protocols, and governance mechanisms can be co-designed to close current capability and safety gaps, outlining critical paths toward more general-purpose, controllable, and accountable multimodal generative systems.