  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.
