Direct measurements of charged cosmic radiation with instruments in Low Earth Orbit (LEO), or flying on balloons above the atmosphere, require the identification of the incident particle, the measurement of its energy and possibly the determination of its sign-of-charge. The latter information can be provided by a magnetic spectrometer together with a measurement of momentum. However, magnetic deflection in space experiments is at present limited to values of the Maximum Detectable Rigidity (MDR) hardly exceeding a few TV. Advanced calorimetric techniques are, at present, the only way to measure charged and neutral radiation at higher energies in the multi-TeV range. Despite their mass limitation, calorimeters may achieve a large geometric factor and provide an adequate proton background rejection factor, taking advantage of a fine granularity and imaging capabilities. In this lecture, after a brief introduction on electromagnetic and hadronic calorimetry, an innovative approach to the design of a space-borne, large acceptance, homogeneous calorimeter for the detection of high energy cosmic rays will be described.