Solar power is already widely used, from individuals with panels on their roof to great solar farms covering acres of land. But the major drawback is the atmosphere, which filters the sunlight, and the weather. Solar power only works when the sun is shining, or when the cloud cover is thin. If the panels could be placed outside the atmosphere those problems would be avoided.
However, solar panels in space have other problems, the first of which is getting them into space in the first place. Current rockets are expensive and the cost of getting large panels into space outweighs the benefits. Most satellites have solar panels for power once they are deployed, but the cost of getting them into space is offset by the benefits of the satellite's function.
Another problem with solar panels is micro meteorites and space debris which cause damage. The cost of solar panels in space has to include regular repairs.
In 1941, science fiction writer Isaac Asimov published the science fiction short story Reason, in which a space station transmits energy collected from the Sun to various planets using microwave beams. A satellite solar-power system (SSPS), was first described in November 1968, and various feasibility studies have been done since then. Mostly they have just identified the many problems faced, but with the pressure of climate change several countries currently have programmes looking at the possibility again.
In 1999, NASA's Space Solar Power Exploratory Research and Technology program (SERT) was initiated. More recently the Japan Aerospace Exploration Agency (JAXA) announced on 12 March 2015 that they wirelessly beamed 1.8 kilowatts 50 meters to a small receiver by converting electricity to microwaves and then back to electricity. On Nov 2, 2012, China proposed space collaboration with India that mentioned, "may be Space-based Solar Power initiative so that both India and China can work for long term association with proper funding along with other willing space faring nations to bring space solar power to earth."
You can read more details in this great article on Wikipedia.
Here is how A Brief History of the Future solves the problem:
In 2176 a Chinese University student built a solar panel modelled on the design of a growing fern. To do this she created a tiny robot which could change its shape from flat to triangular in response to a cascading radio signal. When fifty or more of these micro robots worked together they could unfurl like a fern. These fern panels were improved to be able to furl up again and launched into space as room sized spheres which could extend to cover hundreds of square metres. By 2190 these fern panels were able to repair themselves when damaged by micro meteor strikes.Ann Marie Thomas is the author of four medieval history books, a surprisingly cheerful poetry collection about her 2010 stroke, and the science fiction series Flight of the Kestrel. Book one, Intruders, and book two Alien Secrets, are out now. Follow her at http://eepurl.com/bbOsyz