TensorFlow has been the most widely adopted Machine/Deep Learning framework. However, little exists in the literature that provides a thorough understanding of the capabilities which TensorFlow offers for the distributed training of large ML/DL models that need computation and communication at scale. Most commonly used distributed training approaches for TF can be categorized as follows: 1) Google Remote Procedure Call (gRPC), 2) gRPC+X: X=(InfiniBand Verbs, Message Passing Interface, and GPUDirect RDMA), and 3) No-gRPC: Baidu Allreduce with MPI, Horovod with MPI, and Horovod with NVIDIA NCCL. In this paper, we provide an in-depth performance characterization and analysis of these distributed training approaches on various GPU clusters including the Piz Daint system (6 on Top500). We perform experiments to gain novel insights along the following vectors: 1) Application-level scalability of DNN training, 2) Effect of Batch Size on scaling efficiency, 3) Impact of the MPI library used for no-gRPC approaches, and 4) Type and size of DNN architectures. Based on these experiments, we present two key insights: 1) Overall, No-gRPC designs achieve better performance compared to gRPC-based approaches for most configurations, and 2) The performance of No-gRPC is heavily influenced by the gradient aggregation using Allreduce. Finally, we propose a truly CUDA-Aware MPI Allreduce design that exploits CUDA kernels and pointer caching to perform large reductions efficiently. Our proposed designs offer 5-17X better performance than NCCL2 for small and medium messages, and reduces latency by 29% for large messages. The proposed optimizations help Horovod-MPI to achieve approximately 90% scaling efficiency for ResNet-50 training on 64 GPUs. Further, Horovod-MPI achieves 1.8X and 3.2X higher throughput than the native gRPC method for ResNet-50 and MobileNet, respectively, on the Piz Daint cluster.