Modeling the solar spectral irradiance is necessary for different fields: solar, atmospheric and climate physics. In general, the reconstructions aim to generate the solar spectral irradiance (SSI) at a time where no measurement exists. Therefore, they are based on different solar indicators (named proxies), which have the property to correlate their variations with the SSI variation. The long term reconstructions are used in Climate science to study some particular epochs such as the Maunder minimum or the optima of the Middle age. However, reconstructions can be also used to fill a gap in a SSI time series due to a temporary interruption of an instrument operation in space. As in this case many proxies are available, it is expected that filling the gap by modeling will produce precise results. Reconstructions are also used in the field of Earth and planetary atmosphere physics as the relevant space missions started in the 60's (e.g. the Orbital Geophysical Observatory series), i.e before the solar space missions were able to produce SSI time series. Here also, using moderm proxies allow production of precise SSI, which are the necessary input to the atmophere models. Then, the output of such models are compared to the measurements permitting validation of the photochemical processes implemented in the models. Solar reconstructions employ different means leading to simulations either theoretical, semi-empirical or fully empirical methods. For the past periods, their inputs are generally the sunspots number, the cosmogenic isotopes concentration variation obtained from tree rings, and ice core soundings. These proxies constitute time series more or less without gaps, and have variable accuracy and precision generally time dependent. These proxies are the basic inputs of most of the models.