Weights are arguably one of the most important parts of neural networks, as they determine their functions alongside architectures. Therefore, selecting the appropriate weights when training is key to ensuring that neural networks perform effectively. On the other hand, activations are the result of computations performed by a neural network on input data, and therefore are essential to understand the behavior of neural networks and their properties. The use of TDA to analyze weights and activations is divided into two approaches. The first one, more qualitative, uses Mapper to understand the structure of internal representations of neural networks. The second, more quantitative, uses persistent homology to extract topological features of internal representations of neural networks and link them with different properties of the networks, such as their generalization capabilities.