The Wasserstein distance, originating from optimal transport theory, is a powerful metric for comparing distributions and has been extensively adapted for various domains such as structured data and high-dimensional distributions. Its use in Machine Learning has advanced applications like graph embeddings, adversarial learning, variational autoencoders, and generative models. However, current applications on graphs are limited to static graphs with homogeneous attributes, restricting their utility for heterogeneous or dynamic graphs. This work in progress addresses these limitations by proposing the Attributed Fused Gromov-Wasserstein Distance (AFGWD) for graphs with diverse attribute spaces and the Temporal Fused Gromov-Wasserstein Distance (TFGWD) for discrete- and continuous-time dynamic heterogeneous graphs. Efficient computation strategies using existing approximation methods are discussed to tackle the computational challenges of Wasserstein distances. These advancements aim to broaden the applicability of Wasserstein distances in complex and dynamic graph data scenarios, paving the way for future research.