Social network alignment, aligning different social networks on their common users, is receiving dramatic attention from both academic and industry. All existing studies consider the social network to be static and neglect its inherent dynamics. In fact, the dynamics of social networks contain the discriminative pattern of an individual, which can be leveraged to facilitate social network alignment. Hence, we for the first time propose to study the problem of aligning dynamic social networks. Towards this end, we propose a novel Dynamic social Network Alignment (DNA) framework, a unified optimization approach over deep neural architectures, to unfold the fruitful dynamics to perform alignment. However, it faces tremendous challenges in both modeling and optimization: (1) To model the intra-network dynamics, we explore the local dynamics of the latent pattern in friending evolvement and the global consistency of the representation similarity with neighbors. We design a novel deep neural architecture to obtain the dual embedding capturing local dynamics and global consistency for each user. (2) To model the inter-network alignment, we exploit the underlying identity of an individual from the dual embedding in each dynamic social network. We design a unified optimization approach interplaying proposed deep neural architectures to construct a common subspace of identity embeddings. (3) To address this optimization problem, we design an effective alternating algorithm with solid theoretical guarantees.We conduct extensive experiments on real-world datasets and show that the proposed DNA framework substantially outperforms the state-of-the-art methods.