As I understand it, a day in the Jewish calendar is from sunset to sunset. How is this handled if you are living so far north or south that you have long periods of daylight or darkness?
This affects when Shabbat and yom tov start and end and when you can perform time-bound mitzvot. There are various opinions (some collected here), so this is something you need to consult your rabbi on. Opinions cited there include: use the times for your home city (if you're visiting); use 6PM; use the point when the sun is at its lowest in the sky.
I once learned that you use the time of the nearest Jewish community that has daily sunrise/sunset, but I can't find support for that now.
According to the entry "Calendar" in the Jewish Encyclopedia (Funk & Wagnalls, New York, 1916)
In higher latitudes, where during the summer the sun does not sink below the horizon, and during the winter does not rise above it, the days are counted in summer from midday, i.e. from one upper crossing of the meridian by the sun to the next crossing; in the winter, from midnight to midnight, i.e. from one lower crossing of the meridian by the sun to the next. (Vol. 3, p. 501)