Modal: Might
Modal auxiliary for uncertain possibility, very formal permission, past-tense of "may" in reported speech.
Might is the most tentative modal — the one you use when you are not sure, when you want to sound extra polite, or when you are reporting what someone else thought was possible in the past. If may sits in the middle of the certainty scale, might leans toward the low end: I might go to the party suggests you are genuinely undecided; I may go sounds a bit more likely.
For possibility, might signals low confidence. It might rain tomorrow means it is possible but you would not bet on it. Compare this with could, which suggests a real, tangible possibility, and may, which is slightly more probable. In practice, many speakers blur may and might, but careful writers preserve the distinction: might for the less certain scenario. In third conditional sentences, might replaces may in hypothetical past situations: If you had asked me, I might have helped.
Might is also the past-tense form of may in reported speech. When you shift She may be late into the past, it becomes She said she might be late. This backshifting rule is automatic and essential for accurate reported speech.
For permission, might is the most formal option available — more formal even than may. Might I ask you a few questions? is so polite it borders on deferential. In modern English, this usage is rare outside very formal contexts, but it is worth recognizing when you encounter it.
Might can soften suggestions and criticism. You might want to check the oil is a gentle suggestion — far less direct than You should check the oil. And You might have told me! expresses angry disappointment, implying the listener had every opportunity to speak up but did not. Might also introduces contrasting information politely: He might be talented, but he lacks discipline. Here might concedes a point before delivering the real criticism. Through all these uses, might remains what it has always been: the modal of uncertainty, tact, and careful understatement.
Examples
I'm hoping that she might call me later.
Uncertain possibility
Might I ask you a few questions?
Very formal permission