Placidus
The most widely used house system. It divides each degree's daily travel above and below the horizon by time, so house sizes vary with latitude. The default in most chart software, including ours.
Placidus is a quadrant house system named for Placidus de Titis, a seventeenth-century monk and mathematician, though the method itself is older. Its idea: take the time each point of the zodiac spends above and below the horizon, cut those arcs into thirds, and let the cuts define the intermediate house cusps.
Because the cuts follow time rather than space, Placidus houses are unequal, and the inequality grows with latitude. Far enough north or south, some zodiac degrees never rise or set at all and the system breaks: inside the polar circles Placidus is undefined, which is why our chart falls back to whole sign there.
Its dominance owes a lot to history: for the two centuries when astrologers worked from printed tables, the tables in the back of the book were Placidus tables. But it has real defenders too, and it remains the reference other systems are compared against. If a planet lands within a degree or two of a Placidus cusp, it is worth viewing the chart in whole sign as well.