Information Retrieval (IR) models are a core component of IR research and IR systems. The past decade brought a consolidation of the family of IR models, which by 2000 consisted of relatively isolated views on TF-IDF (Term-Frequency times Inverse-Document-Frequency) as the weighting scheme in the vector-space model (VSM), the probabilistic relevance framework (PRF), the binary independence retrieval (BIR) model, BM25 (Best-Match Version 25, the main instantiation of the PRF/BIR), and language modelling (LM). Also, the early 2000s saw the arrival of divergence from randomness (DFR). Regarding intuition and simplicity, though LM is clear from a probabilistic point of view, several people stated: ""It is easy to understand TF-IDF and BM25. For LM, however, we understand the math, but we do not fully understand why it works."" This book takes a horizontal approach gathering the foundations of TF-IDF, PRF, BIR, Poisson, BM25, LM, probabilistic inference networks (PIN's), and divergence-based models. The aim is to create a consolidated and balanced view on the main models. A particular focus of this book is on the ""relationships between models."" This includes an overview over the main frameworks (PRF, logical IR, VSM, generalized VSM) and a pairing of TF-IDF with other models. It becomes evident that TF-IDF and LM measure the same, namely the dependence (overlap) between document and query. The Poisson probability helps to establish probabilistic, non-heuristic roots for TF-IDF, and the Poisson parameter, average term frequency, is a binding link between several retrieval models and model parameters.