What lays beyond the walls? I've always wondered what really lies beyond the walls. The most we've seen of the area outside is the Female Titan arc and the scene that played before the theme in episode 1 of the anime. Both times, we didn't get to see much of anything besides lots of trees. 

What else is out there? Old remnants of villages existing before the titans? Other walled countries?
The Female Titan arc (57th expedition) DOES NOT take place beyond the walls. It takes place in the area between Wall Maria and Wall Rose, so anything we see there is just a part of the lost territory within the walls. This also includes when we first met Levi and his squad, because the 56th expedition took place from Trost since Maria had already fallen.

MAJOR SPOILERS FROM CHAPTER 85 AND 86 OF THE MANGA


   As it turns out, the walls are on an island called Paradis, with a sizeable amount of land between the walls and the island's coast, but a mainland off the west coast of Paradis is home to humans (the Eldian and Marleyan ethnicities) and is not infested with Titans as Paradis is.