Previous embedding methods for attributed networks aim at learning low-dimensional vector representations only for nodes but not for both nodes and attributes, resulting in the fact that node embeddings cannot be directly used to recover the correlations between nodes and attributes. However, capturing such correlations by embeddings is of great importance for many real-world applications, such as attribute inference and user profiling. Moreover, in real-world scenarios, many attributed networks evolve over time, with their nodes, links, and attributes changing from time to time. In this article, we study the problem of jointly learning low-dimensional representations of both nodes and attributes for static and dynamic attributed networks. To address this problem, we propose a Co-embedding model for Static Attributed Networks (CSAN), which jointly learns low-dimensional representations of both attributes and nodes in the same semantic space such that their affinities can be effectively captured andmeasured, and a Co-embedding model for Dynamic Attributed Networks (CDAN) to dynamically track low-dimensional representations of nodes and attributes over time. To obtain effective embeddings, both our co-embedding models, CSAN and CDAN, embed each node and attribute with means and variances of Gaussian distributions via variational auto-encoders. Our CDAN model formulates the dynamic changes of a dynamic attributed network by aggregating perturbation features from the nodes' local neighborhoods as well as attributes' associations such that the evolving patterns of the given network can be tracked. Experimental results on real-world networks demonstrate that our proposed embedding models outperform state-of-the-art non-dynamic and dynamic embedding models.