The chromospheric temperature rise to values above the photospheric temperature cannot be due to radiative energy transport alone. We will outline different possibilities for the additional energy transport in the solar atmosphere by processes that require (or exclude) the presence of magnetic fields. We will discuss which of them could be identified and studied in detail using current data. To find the signature of the different heating processes and derive quantitative estimates of their efficiency, we analyzed simultaneous spectropolarimetric observations of photospheric magnetic fields (@630 nm) and intensity spectra of the chromospheric Ca II H line (396 nm). The mechanical energy flux at several height layers was derived from the velocity amplitudes of propagating acoustic waves seen in different spectral lines. The enhancement of chromospheric (radiation) temperature above the radiative equilibrium values was taken from an inversion of the Ca II H spectra with the SIR code assuming local thermal equilibrium (LTE) and complete redistribution (CRD). We compare the obtained energy values with each other and with the energy requirements demanded by theoretical/semi-empirical atmospheric models. We find that the most important agent of chromospheric heating are propagating (magneto-)acoustic waves, which suffice to explain the brightenings in Ca II H spectra and their corresponding temperature enhancements. The energy contained in these intensity variations of the Ca II H line, however, is found to be insufficient to maintain a full-time and full-volume "hot" chromosphere. Additional energy transport mechanisms without a signature in the Ca II H spectra are thus necessary. Finally, we will outline which improvements are to be expected with future observations of higher quality (spatial resolution, enhanced polarimetric sensitivity, temporal cadence, other spectral lines) to be achieved with new ground-based telescopes like GREGOR or EST.