This is not an extensive technical discussion of houses, but a look at several major issues regarding them. I'm not a particularly mathematical astrologer, thus seek to understand the principles of of Astrology in relatively simple terms.
Houses are arguably the most contested area of basic astrological practice.
There are well over a dozen house systems, as well as disagreement about the significance of a house cusp. Few astrologers understand the underlying symbology of the houses because the construction of most systems is much more abstract than the calculation of planets' positions in the Zodiac. The Placidus system is the most popular one in the western world, its success based as much on widespread publication and distribution of its tables as its efficacy. In fact, most systems use the Midheaven as the cusp of the 10th house and the Ascendant as the cusp of the 1st. The differences come in the calculations of the other house cusps, called the intermediate houses.