The Sun is the main energy source to Earth, and understanding its variability is of direct relevance to climate studies. Measurements of total solar irradiance (TSI) exist since 1978, but this is too short compared to climate-relevant time scales. Coming from a number of different instruments, these measurements require a cross-calibration, which is not straightforward, and thus several composite records have been created. All of them suggest a marginally decreasing secular trend in solar minima levels since 1996. Most composites actually feature a weak decrease over the entire period of observations, which is also seen in observations of the solar surface magnetic field and is further supported by Caii Kdata. Some inconsistencies, however, remain and overall the magnitude and even the presence of the secular change over the satellite era remain uncertain. Different models have been developed, which are used to understand the irradiance variability over the satellite period and to extend the records of solar irradiance back in time. Differing in their methodologies, all models require proxies of solar magnetic activity as input. The most widely used proxies are sunspot records and cosmogenic isotope data on centennial and millennial time scale, respectively. None of this, however, offers a sufficiently good, independent description of the long-term evolution of faculae and network responsible for solar brightening. This leads to significant uncertainties in the amplitude of the changes in solar irradiance on time scales longer than the solar cycle. Here we review recent efforts and advances aiming at improving long-term irradiance reconstructions and to reduce the existing uncertainty in the magnitude of the long-term variability. In particular, by employing state-of-the-art 3D magnetohydrodynamical simulations, an upper limit of 2±0.7 Wm−2 was set on the possible increase of TSI since the end of the Maunder minimum as compared to the 2019 minimum level. Besides, significant progress has been made in collecting and processing historical solar observation in Caii Kspectral line, which provide direct information on bright magnetic features on the Sun and can be used to improve the accuracy of past irradiance reconstructions, pending some remaining issues with the data.