We use the SPace Infrared telescope for Cosmology and Astrophysics (SPICA) project as a template to demonstrate how deep spectrophotometric surveys covering large cosmological volumes over extended fields (1- ) with a mid-IR imaging spectrometer (17- ) in conjunction with deep photometry with a far-IR camera, at wavelengths which are not affected by dust extinction can answer the most crucial questions in current galaxy evolution studies. A SPICA-like mission will be able for the first time to provide an unobscured three-dimensional (3D, i.e. x, y, and redshift z) view of galaxy evolution back to an age of the universe of less than 2 Gyrs, in the mid-IR rest frame. This survey strategy will produce a full census of the Star Formation Rate (SFR) in the universe, using polycyclic aromatic hydrocarbons (PAH) bands and fine-structure ionic lines, reaching the characteristic knee of the galaxy luminosity function, where the bulk of the population is distributed, at any redshift up to . Deep follow-up pointed spectroscopic observations with grating spectrometers onboard the satellite, across the full IR spectral range (17- -3), through IR emission lines and features that are insensitive to the dust obscuration.