This paper presents novel solutions for the efficient and reliable transmission of point clouds over wireless channels for real-time applications. We first propose SEmatic Point cloud Transmission (SEPT) for small-scale point clouds, which encodes the point cloud via an iterative downsampling and feature extraction process. At the receiver, SEPT decoder reconstructs the point cloud with latent reconstruction and offset-based upsampling. A novel channel-adaptive module is proposed to allow SEPT to operate effectively over a wide range of channel conditions. Next, we propose OTA-NeRF, a scheme inspired by neural radiance fields. OTA-NeRF performs voxelization to the point cloud input and learns to encode the voxelized point cloud into a neural network. Instead of transmitting the extracted feature vectors as in SEPT, it transmits the learned neural network weights in an analog fashion along with few hyperparameters that are transmitted digitally. At the receiver, the OTA-NeRF decoder reconstructs the original point cloud using the received noisy neural network weights. To further increase the bandwidth efficiency of the OTA-NeRF scheme, a fine-tuning algorithm is developed, where only a fraction of the neural network weights are retrained and transmitted. Noticing the poor generality of the OTA-NeRF schemes, we propose an alternative approach, termed OTA-MetaNeRF, which encodes different input point clouds into the latent vectors with shared neural network weights. Extensive numerical experiments confirm that the proposed SEPT, OTA-NeRF and OTA-MetaNeRF schemes achieve superior or comparable performance over the conventional approaches, where an octree-based or a learning-based point cloud compression scheme is concatenated with a channel code. Finally, the run-time complexities are evaluated to verify the capability of the proposed schemes for real-time communications.