Adjusting the house to the landscape is the first task to be solved when building on difficult terrain. If your block of land has slopes up to 20% - it's rather regular terrain. The difficulties start to appear on slopes that are steeper than that.
Main problems can be divided into 3 categories:
1) Some additional research to determine the danger of soil slipping down should be done
2) The foundations and plumbing will require some additional work
3) Some additional work to level the soil might be necessary
And of course any of above translates into additional expenses.
If the allotment is in a real danger of soil slip, for example the soil has a steep rocky slope underneath and gets lots of rainfall or has ground water - it makes no sense to build on it.
However, if that's not the case, then building on steep slope might produce very interesting outcome. History has many examples of people, who had to deal with difficult conditions, created the most magnificent structures, some of which we can still see in these days. They include the Machu Picchu city in Peru, great castles of Europe, Svan's watchtowers in high mountains of Georgia, and fort Metsada in Israel.
To make the idea of building on difficult terrain a reality, several things need to fall together:
1) The wish to build on this particular block of land and the ability to finance the process
2) A talented architect and engineer who can fit the house into the relief while making it secure, safe and sound
3) Qualified builders who can implement everything according to the plans
So what are the advantages of building on a slope? First, nothing compares to the panoramic view from your terrace. Also, it is possible to create several levels: the garage on the upper level, the bedrooms and living areas below and the back yard and garden on the lowest level. The best thing about this setting is that the road and the driveway - with all the noise and the dust - are left on top, while the house is located below. More of the house is now exposed to the sun light. The garden can have many picturesque features such as little terraces, steps, miniature walls, cozy spots.
The whole presence of the house is improved, as this unique facade is created. The interior of the house benefit from larger windows and various open staircases, they look "weightless" and mix in harmony with the nature.
Another issue to address is the soundness of the house built on a slope. In many ways it depends on the soil underneath the foundations. If the soil is mostly sand or mud, then it makes sense to create terraced foundations, made of concrete bands and retaining walls, anchored in the soil.
If the foundations are to be built on rocks, concrete piles are better. The necessary diameter of a pile for 2 -3 level house is 35 - 40 cm, the depth is 8 to 10 meters. A reinforcing cage is installed in the borehole, which is later filled with concrete. The maximal load is to be defined by the engineer. All of the above methods are intended for brick and concrete houses. The foundations are much simpler to make for lighter houses.
Steep slopes are not the only kind of difficult terrain. One of the world-famous masterpieces - Frank Lloyd Wright's "Fallingwater" - is a house built on top of a cliff with a waterfall rushing underneath. Its multilevel terraces are floating above the waterfall in the air filled with freshness of a creek. Buildings that are so much in harmony with the nature around are usually well-planned and well-built ones.
Another example of such building is the famous Sydney Opera house - a caravel with wind-filled sails in the open ocean. However, the story of those sails has no happy ending: the author of the project that won a contest, architect Jorn Utzon, originally intended for the construction to look similar to wind-filled sails. Unfortunately, the calculations and the construction couldn't be done according his project, which is why the current looks of the Opera House, is very different from the way it meant to be.