Water Inside
Water showing up on a chimney breast or beside the fireplace has five possible routes, and the fix is completely different for each.
Short answer
Through the top where the crown has failed or there is no cap; through the masonry itself where it is saturated; through the flashing at the roof line; through condensation inside the flue; and through the flue from an appliance producing condensate. Timing and location point to which one.
The five routes
Down the flue from the top: a failed crown, no cap, or cracked tiles at the top. Shows as water in the firebox and a rusted damper.
Through the masonry: saturated brick releasing water inward. Shows as damp and efflorescence on the chimney breast, appearing days after rain rather than during it.
Through the flashing at the roof line: step flashing, counter flashing or a missing cricket. Shows as staining on the ceiling beside the chimney.
Condensation inside the flue: an oversized or cold flue where the flue gases condense. Shows as staining when the appliance is in use rather than when it rains.
An appliance producing condensate venting into a masonry flue, which is the modern gas version of the same thing.
And a sixth that is not the chimney at all: a roof leak elsewhere running along framing and appearing at the chimney, which is the chimney getting blamed.
Timing tells you which
During rain and heavy rain: flashing or the top. A day or two after rain: the masonry absorbing and releasing. In cold weather with the appliance running and no rain: condensation inside the flue. With wind from one direction: flashing on that face. Note the timing before anybody quotes anything.
What to check
The crown, from the roof or from a photograph taken from a ladder, for cracks and whether it is a crown or a mortar wash.
Whether there is a cap.
The flashing: step flashing woven into the courses, counter flashing cut into a mortar joint, and a cricket behind a wide stack.
The pointing and the brick faces, for open joints and spalling.
The firebox and the damper, for water staining and rust, which indicates the top route.
And the attic beside the chimney during rain, which is where the flashing route is visible.
The order to fix it
Cap and crown first, because they are the cheapest and the most likely.
Flashing next, done properly with metal in layers rather than cemented.
Pointing, with a compatible mortar.
The liner, where the flue is the route or the size is wrong.
A breathable repellent on the masonry last, once everything else is sound.
And resist a quote that starts with the repellent, because that is the one thing that is almost never the actual answer on its own.
Common questions
How do I tell which route it is?
Note the timing. During rain points at the flashing or the top; days later points at the masonry.
What should be fixed first?
The cap and the crown. Cheapest and most likely.
Could it be a roof leak somewhere else?
Yes. Water runs along framing and the chimney gets blamed.