Our current knowledge of star formation and accretion luminosity at high-redshift (z>3-4), as well as the possible connections between them, relies mostly on observations in the rest-frame ultraviolet (UV), which are strongly affected by dust obscuration. Due to the lack of sensitivity of past and current infrared (IR) instrumentation, so far it has not been possible to get a glimpse into the early phases of the dust-obscured Universe. Among the next generation of IR observatories, SPICA, observing in the 12-350 micron range, will be the only facility that can enable us to make the required leap forward in understanding the obscured star-formation rate and black-hole accretion rate densities (SFRD and BHARD, respectively) with respect to what Spitzer and Herschel achieved in the mid- and far-IR at z<3. In particular, SPICA will have the unique ability to trace the evolution of the obscured SFRD and BHARD over cosmic time, from the peak of their activity back to the reionisation epoch (i.e., 3 < z < 6 - 7), where its predecessors had severe limitations. Here we discuss the potential of both deep and shallow photometric surveys performed with the SPICA mid-IR instrument (SMI), enabled by the very low level of impact of dust obscuration in a band centred at 34 micron. These unique unbiased photometric surveys that SPICA will perform will be followed up by observations both with the SPICA spectrometers and with other facilities at shorter and longer wavelengths, with the aim to fully characterise the evolution of AGNs and star-forming galaxies after re-ionisation.< Réduire