Recently, heatmap regression methods based on 1D landmark representations have shown prominent performance on locating facial landmarks. However, previous methods ignored to make deep explorations on the good potentials of 1D landmark representations for sequential and structural modeling of multiple landmarks to track facial landmarks. To address this limitation, we propose a Transformer architecture, namely 1DFormer, which learns informative 1D landmark representations by capturing the dynamic and the geometric patterns of landmarks via token communications in both temporal and spatial dimensions for facial landmark tracking. For temporal modeling, we propose a confidence-enhanced multi-head attention mechanism with a recurrently token mixing strategy to adaptively and robustly embed long-term landmark dynamics into their 1D representations; for structure modeling, we design intra-group and inter-group geometric encoding mechanisms to encode the component-level as well as global-level facial structure patterns as a refinement for the 1D representations of landmarks through token communications in the spatial dimension via 1D convolutional layers. Experimental results on the 300VW and the TF databases show that 1DFormer successfully models the long-range sequential patterns as well as the inherent facial structures to learn informative 1D representations of landmark sequences, and achieves state-of-the-art performance on facial landmark tracking. Codes of our model are available in the supplementary materials.