Understanding propagation mechanisms in complex networks is essential for fields like epidemiology and multi-robot networks. This paper reviews various propagation models, from traditional deterministic frameworks to advanced data-driven and deep learning approaches. We differentiate between static and dynamic networks, noting that static models provide foundational insights, while dynamic models capture real-world temporal changes. Deterministic models like the SIR framework offer clear mathematical insights but often lack adaptability to randomness, whereas stochastic models enhance realism at the cost of interpretability. Behavior-based models focus on individual decision-making, demanding more computational resources. Data-driven approaches improve accuracy in nonlinear scenarios by adapting to evolving networks, using either traditional models or model-free machine learning techniques. We explore supervised and unsupervised learning methods, as well as reinforcement learning, which operates without predefined datasets. The application of graph neural networks (GNNs) is also discussed, highlighting their effectiveness in modeling propagation in complex networks. The paper underscores key applications and challenges associated with each model type, emphasizing the increasing importance of hybrid and machine learning-based solutions in contemporary network propagation issues.