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 trend since 1996. Most composites also 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 Ca ii K data. Some inconsistencies, however, remain and overall the magnitude and even the presence of the long-term trend 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 long-term changes in solar irradiance. Here we review recent efforts to improve irradiance reconstructions on time scales longer than the solar cycle and to reduce the existing uncertainty in the magnitude of the long-term variability. In particular, we highlight the potential of using 3D magnetohydrodynamical simulations of the solar atmosphere as input to more physical irradiance models and of historical full-disc Ca ii K observations encrypting direct facular information back to 1892.