Research shows that 66.54 percent of children aged between 29 months and six years occasionally suffer from nightmares, while 2.16 percent often have bad dreams.  Nightmares can be caused by a variety of factors, including the processing of stressors, behavioral problems, and sleep disorders. Anxiety in children, however, has been found to be among the most common causes of frequent bad dreams they experience. 
How Are Nightmares And Night Terrors Defined?
We're all familiar with the term "nightmare", so readers may be asking themselves why their definition needs to be discussed at all. It's important to note, though, that clinical definitions can get in the way of adequately studying how many kids are affected by them — the fourth version of the Diagnostic and Statistical Manual defined nightmares as "extremely frightening dreams from which the person wakes up directly". Researchers point out that this definition is rather narrow. Nightmares may involve anger, grief and other difficult emotions in addition to fear, and they can cause enormous distress even in children who are not awoken during their bad dreams.  Failing to acknowledge this broader definition may mean that the prevalence of nightmares is underestimated.
Night terrors are, on the other hand, a completely different beast. Unlike nightmares, they occur during non-REM sleep in the first three or four hours after a person has fallen asleep. Between one and six percent of children are thought to suffer from night terrors, which induce feelings or terror and dread.  While night terrors are not specifically correlated with anxiety in children, both anxiety disorders and post traumatic stress disorder have been found to contribute to night terrors in adults, so we cannot rule out that they are a sign of anxiety in children as well .
Nightmares: Only One Part Of The Diagnostic Picture Of Childhood Anxiety
There are lots of different childhood anxiety disorders, including specific phobias, separation anxiety disorder, obsessive compulsive disorder, social phobia, agoraphobia, panic disorder, and generalized anxiety disorder. 
Let's take a very brief look at the defining symptoms of some of these anxiety disorders :
- Generalized anxiety disorder: Excessive worry and fear about all kinds of events, ranging from earthquakes or terrorist attacks to school performance, which causes significant impairment in completing daily activities.
- Separation anxiety disorder: Separation anxiety in children is manifested through excessive and distressing worry and fear about being away from attachment figures, typically parents.
- Obsessive compulsive disorder: Child feels compelled to engage in certain rituals, such as frequent hand washing and neatly organizing their surroundings, in order to "prevent catastrophe from occurring".
- Social phobia: Anxiety related to social situations, not just with unfamiliar adults but also with peers.
- Specific phobias: Great fear of specific things, such as spiders or dogs, which may manifest itself when not directly confronted with the feared object as well.
These anxiety disorders can additionally lead to physical symptoms such as headaches, tummy aches, nausea, muscle tension, fatigue, and low energy. 
Not all children who have frequent nightmares suffer from anxiety — data suggests that independent sleep disorders such as insomnia, disordered breathing during sleep, and sleep walking, along with genetic disposition (parents who also suffer from frequent nightmares) are likewise associated with frequent bad dreams. 
Since children who suffer from anxiety were found to have nightmares much more often than those who do not struggle with anxiety, however, research also indicates that nightmares alone are indeed a reason to start examining whether a child might be suffering from an anxiety disorder.  One study, indeed, found that 83 percent of children diagnosed with anxiety disorders suffered from at least one frequent sleep complaint , whether insomnia, excessive daytime sleepiness, sleep walking, night terrors, bedwetting, or nightmares.
What Should I Do About My Child's Nightmares?
Whether your child's nightmares or night terrors are caused by anxiety or something else, you will want to get to the bottom of the underlying reason for their night-time suffering. If an anxiety disorder is found to be at the root, research shows that a combination of family therapy (where parents also learn the skills they need to help their anxious child) and cognitive behavioral therapy has very favorable results . Where necessary, anxiety medication can also help. Fluoxetine has been found to be among the most well-tolerated medications used for anxiety in children.