The visual relationship recognition (VRR) task aims at understanding the pairwise visual relationships between interacting objects in an image. These relationships typically have a long-tail distribution due to their compositional nature. This problem gets more severe when the vocabulary becomes large, rendering this task very challenging. This paper shows that modeling an effective message-passing flow through an attention mechanism can be critical to tackling the compositionality and long-tail challenges in VRR. The method, called RelTransformer, represents each image as a fully-connected scene graph and restructures the whole scene into the relation-triplet and global-scene contexts. It directly passes the message from each element in the relation-triplet and global-scene contexts to the target relation via self-attention. We also design a learnable memory to augment the long-tail relation representation learning. Through extensive experiments, we find that our model generalizes well on many VRR benchmarks. Our model outperforms the best-performing models on two large-scale long-tail VRR benchmarks, VG8K-LT (+2.0% overall acc) and GQA-LT (+26.0% overall acc), both having a highly skewed distribution towards the tail. It also achieves strong results on the VG200 relation detection task. Our code is available at https://github.com/Vision-CAIR/ReITransformer.