<p>Characterisation of subsurface hydrocarbon flow is central to understanding reservoir behaviour, and reservoir simulation has emerged as an indispensable tool in this context. Compared to experimental approaches, reservoir simulation does not require large capital investments or extensive physical facilities, while still offering significant insights into reservoir performance. It plays a critical role throughout the life cycle of a reservoir, from primary recovery to field abandonment, by enabling engineers to analyse coupled geological, hydrodynamic, and thermal effects on hydrocarbon production. Recent technological advancements have resulted in the development of several commercial and open-source simulation packages that simplify many routine tasks for reservoir engineers. However, effective and reliable use of these tools demands a strong understanding of the underlying conceptual, mathematical, and numerical models. Without this foundation, model predictions may be misinterpreted, leading to unreliable forecasts of oil recovery. This article presents a systematic explanation of the fundamental conceptual, mathematical, and numerical frameworks used in reservoir simulation. It highlights the role of mathematical principles in formulating governing equations and in estimating key parameters across different spatial and temporal scales. Particular emphasis is placed on the necessity of model verification and validation, as forecasting without these steps can result in erroneous reservoir characterisation. The primary contribution of this work is to elucidate the importance of fundamentals and to serve as a structured starting point for engineers and early-stage researchers entering the field of reservoir simulation and subsurface flow modelling.</p>