Note that since radio waves can penetrate dust, they were used to determine the overall structure of the otherwise dusty (and therefore visibly opaque) Milky Way Galaxy. See this link for further information.
The Very Large Array (VLA), by comparison, is an excellent example of the second solution. Located in New Mexico, the VLA consists of 27 identical radio dishes of 25 meters diameter. They are arrayed in a "Y" shaped pattern of 3 spokes, with each spoke 13 miles in length. Using interferometry, the VLA achieves a remarkable radio wave resolution of 0.05 arcseconds, the same as the Earth-orbit-based Hubble Space Telescope obtains for vislble light.
Regarding the first solution, the largest radio telescope in the world (and the largest telescope in the world, period) is the Arecibo Observatory in Puerto Rico. Its main dish is an astounding 305 meters in diameter. Arecibo was instrumental in the discovery of pulsars, or spinning neutron stars.
This "problem" can be solved in one of two ways: 1) make radio telescopes with very large primary mirrors, or 2) use multiple radio telescopes and interferometry to simulate a very large radio telescope.
The "problem" with using radio waves for astronomical observations is that their wavelengths are much longer than those of visible light. As a result, falsely-colored images concocted from them have noticeably poor detail resolution, compared to visible light images.
Besides visible light, radio waves are the only other "type" of electromagnetic radiation that consistently penetrates the Earth's atmosphere. Therefore, Earth-bound radio wave observatories are a critical component of astronomical observation.