Watch it in the rain once and the cause usually narrows to one of these.
Overflows everywhere, even in light rain
A clog. Either the trough is full of leaves and needles, or the downspout below is packed and the gutter has nowhere to drain. Tap the downspout: a dull sound low down means it is full. A cleaning with the downspouts flushed fixes it.
Overflows in the middle of a run
The gutter has sagged there and holds water, or it was hung with the pitch running the wrong way. Standing water a day after rain is the tell. The fix is rehanging on new hangers at the right pitch; see gutter repair.
Overflows at one corner in hard rain only
A valley empties two roof planes into that corner, or the corner is too far from a downspout. Water that hits the outside of a corner at speed jumps the gutter. Fixes: a splash guard at the corner, a downspout closer to it, or a larger gutter on that run. The calculator shows how much water that corner carries at your city's design downpour.
Overflows along the whole run in hard rain only
The gutter or the downspouts are small for the roof section. In metro Atlanta the five-minute downpour expected once in ten years falls at about 8 inches an hour (NOAA Atlas 14). More downspouts or larger ones often solve it before a larger gutter is needed.
Water down the wall behind the gutter
That is not overflow but a gap between the roof edge and the gutter: a missing or short drip edge or gutter apron, or a gutter hung too low on the fascia. It rots the fascia first; see fascia and soffit.