Graph Neural Networks (GNNs) are designed to perform tasks on non-Euclidean relational data, with a myriad of applications. Nonetheless, most GNN architectures are built on the message-passing paradigm, which may lead to poor performance in heterophilic settings and indistinguishable representations as more layers are added, a phenomenon known as oversmoothing. Sheaf Neural Networks (SNNs) can be seen as a natural extension of GNNs, enabling the modeling of topological and geometrical inductive biases inherent in structured data. The modulated message passing mechanism within the cellular sheaf structure allows for more expressive interaction between nodes, which can circumvent the homophily assumption and mitigate oversmoothing, issues that commonly arise on graphs. The present work aims to introduce some of the principal recently developed architectures of SNNs, leveraging new versions of well-known GNN models, convolutional and attentional, as well as novel sheaf-based diffusion models. We also give a glimpse of how sheaves are being used in other contexts beyond traditional graph tasks.