There are at least two bands with this name:

1) Dreamscape is a German progressive metal band, founded by lead guitarist Wolfgang Kerinnis and rhythm guitarist Stefan Gassner in 1986. After countless changes in the line-up, singer Tobi Zoltan, drummer Andreas Angerer and bassist Benno Schmidtler stayed with them.
After very thorough preparations, they started performing live in 1992. After more line-up changes, they produced three demos in between 1993 and 1995 called Dreamscape, Decisions, and Changes. After that, in their own studio, the band recorded their first album, Trance-like State in 1996 and was released through Rising Sun Records twelve months later in 1997. In the wake of the CD production, several changes took place. The band decided that they needed a keyboardist as a permanent member.
After a while, Jan Vacik ended up filling the keyboard spot. The permanent keyboardist caused three members to leave, one of them being founding member Stefan Gassner. During those twelve months in between recording and releaseing, Dreamscape already thought up new songs. However, they were being delayed once more because Tobi Zoltan, the vocalist at the time, was asked to leave due to lack of motivation. Soon afterwards, Hubi Meisel replaced Zoltan as vocalist. After touring, Dreamscape came out with their second album Very in 1999. Since then, there have been multiple line-up changes and Dreamscape has released two studio albums and one compilation album.

2) Dreamscape was an obscure dream pop band from Bristol, England, UK, active between 1990 and 1993. Guitarist Scott Purnell, bassist Jamie Gingell, and singer Rebecca Rawlings released two EPs in 1991 and 1992. It was during this time that Purnell and Gingell were working on a side project without Rawlings, named Secret Shine. After sending Sarah Records their shambolic demo, Secret Shine was picked up and Dreamscape faded into obscurity.

3) A weekly podcast, filled with electronic and cosmic music. Hosted by well known Dutch artist Ron Boots. Download: http://radio.groove.nl/ Read more on Last.fm. User-contributed text is available under the Creative Commons By-SA License; additional terms may apply.