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Solar flares are transient yet dramatic events in the atmosphere of the Sun, during which a vast amount of magnetic energy is liberated. This energy is subsequently transported through the solar atmosphere or into the heliosphere, and together with coronal mass ejections flares comprise a fundamental component of space weather. Thus, understanding the physical processes at play in flares is vital. That understanding often requires the use of forward modelling in order to predict the hydrodynamic and radiative response of the solar atmosphere. Those predictions must then be critiqued by observations to show us where our models are missing ingredients. While flares are of course 3D phenomenon, simulating the flaring atmosphere including an accurate chromosphere with the required spatial scales in 3D is largely beyond current computational capabilities, and certainly performing parameter studies of energy transport mechanisms is not yet tractable in 3D. Therefore, field-aligned 1D loop models that can resolve the relevant scales have a crucial role to play in advancing our knowledge of flares. In recent years, driven in part by the spectacular observations from the Interface Region Imaging Spectrograph (IRIS), flare loop models have revealed many interesting features of flares. For this review I highlight some important results that illustrate the utility of attacking the problem of solar flares with a combination of high quality observations, and state-of-the-art flare loop models, demonstrating: (1) how models help to interpret flare observations from IRIS, (2) how those observations show us where we are missing physics from our models, and (3) how the ever increasing quality of solar observations drives model improvements. Here in Paper 1 of this two part review I provide an overview of modern flare loop models, and of electron-beam driven mass flows during solar flares.