KL divergence, or relative entropy, is a metric used to compare two data distributions in data science, assessing dataset and model drift, information retrieval for generative models, and reinforcement learning. It measures the statistical distance between two probability distributions, quantifying how much they differ from each other. The lower bound value of KL divergence is zero, achieved when the distributions are identical. This metric is asymmetric, meaning that given a probability distribution P and a probability distribution Q, the divergence between P and Q is not the same as Q and P. KL divergence is defined as the number of bits required to convert one distribution into another and closely resembles the cross-entropy loss function used in deep learning. It is applied to data in discrete form by forming data bins and summed up to get a final picture. In neural networks, it serves as a loss function to compare predicted distributions with true labels, optimizing to bring the divergence value down to zero. Variational auto-encoders use KL divergence to calculate the statistical distance between the true distribution and the approximating distribution, while generative adversarial networks use it to create a comparable metric to evaluate whether the model is learning. However, KL divergence has certain drawbacks, including its asymmetric behavior and unstable training dynamics, making Jensen-Shannon Divergence a better fit in some cases.