Understanding foreground emission at low radio frequencies touches upon many fundamental questions in astrophysics. With the novel low-frequency radio telescopes researchers are expected to detect cosmological radiation emitted billions of years ago, from the time of the first “stars”. These very deep observations will not only set constraints on when and where the first sources formed in the early Universe and began (re)ionizing the predominantly neutral all-pervasive intergalactic medium, but they are also providing high-quality data for cutting edge auxiliary foreground science. Obviously studying the physical origin of the foregrounds, whether Galactic or extragalactic, is a very exciting field in its own right and is of fundamental importance for perfecting the foreground removal techniques in the cosmological experiments. Here, we propose the state-of-the-art study of the foreground emission. In particular, we will: (i) use the novel capabilities of the Low Frequency Array (LOFAR) radio telescope to conduct the detailed tomography of the local interstellar medium (ISM) by observing Galactic synchrotron emission and its polarization; (ii) combine these radio observations with other observational probes (e.g. HI, H?, dust, GRB afterglows, close-by stars, etc.) to investigate the association of Faraday structures with different ISM phases and association with the interstellar magnetic fields; (iii) built new data driven model of Galactic polarized emission that will be used for development of the foreground removal techniques; and (iv) simulations of extragalactic radio sources, based on the Cosmic Evolution Survey (COSMOS) results. Funding of the proposed research is essential to keep Croatian astrophysics at an internationally competitive level and go beyond this by providing results that will pave the way for the key science cases of the next generation of radio telescopes (e.g. Square Kilometer Array).