It can deal with themes like war, genocide, and death.
Some episodes do contain moderately intense themes, scary elements, or frightening images. While these moments occur within various adventures, nothing in the series ever becomes outright horrific.
The weeping angels have some mildly scary episodes, as they can only move when no one is looking at them... so if a person blinks... they have quite a few jumpscares.
Some episodes have jump scares and generally intense moments.
Series finales usually have very frightening scenes, (especially series 10's)
The show has a history of giving its younger audience members a bit of a scare so each season usually has one or two horror episodes. These episodes engage in effective scares and tension, but the horror never leans into anything explicit or graphic.
Blink (Series 3 Episode 10) has a very scary suspenseful scene as The Doctor apprises two characters about the Weeping Angels, and tells them how dangerous they are, and encourages them not to blink.
The Cybermen have a very dark background as they are people who have their brains trapped inside, and stripped off all emotions, as emotions would cause them to freak out so much they die. The cyberman also are relentless and near impossible to kill. They shock people to the point of death.
Some monster designs may frighten young viewers. Such as the Flood, the Weeping Angels and the Gangers.