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This came up in regards to the Dominate Person spell in session today.
Dominate Person (as well as Charm Person, and also the other two Dominate spells, and perhaps others?) states the following (PHB 235 with my emphasis):

You attempt to beguile a humanoid that you can see within range. It must succeed on a Wisdom saving throw or be charmed by you for the duration. If you or creatures that are friendly to you are fighting it, it has advantage on the saving throw.

What does fighting mean?

Some options would be:

1. In an encounter with the potential for combat.


2. 
   Actively engaged in combat. Different than #1. For example at the start of an encounter, a bard with high DEX goes first in initiative order and decides to cast Dominate Person on someone in the opposing group. However no one in either group has actually engaged in fighting anyone since the bard is first. She could also choose to talk and be diplomatic, would that be considered fighting because it happens during an encounter?


3. Have been engaged in combat with, but are not currently (i.e. castle guards that might be looking for you sneaking about)


4. People who are part of a group that you and companions are at odds with and have fought members of, but have not specifically fought the current target of the spell (i.e. a member of an opposing thieves' guild)


5. Anyone who is at odds with you or someone friendly to you


6. A verbal argument with someone

There are many specific situations that could be referenced. What I would like to know is:

How is Fighting defined by RAW?

I'll settle for RAI if there is no RAW. And sagely commentary if there is no published indications of RAI.

The D&D 5e Player's Handbook, chapter 9, refers to fighting as what happens during combat, which according to the "Combat Step by Step" sidebar is that familiar situation in which initiative is rolled and everyone takes turns:

When everyone invited in the combat has had a turn, the round ends. Repeat step 4 until the fighting stops.

However, the rules don't strictly define "fighting", meaning that it's also plausible that the DM adjudicates the term under the standardly understood English definition of the word, engaging in a fight. Since a fight is precisely what happens in combat when initiative is rolled, this has the same meaning.

Dungeons and Dragons 5th edition is written in natural English. When a term doesn't have a special definition, we use the normal English definition of the word. Even when a word is defined, its meaning generally aligns with its normal definition. While 'fighting' has numerous possible related definitions, the one which makes most sense in the context of D&D, a game centred around combat, is

Take part in a violent struggle involving the exchange of physical blows or the use of weapons.

(Source: Oxford Dictionaries)

In the spell you quote, 'fighting' is used in the present tense. As such, it only refers to a fight which is happening at the time of casting. But when does a fight start or stop?

In Dungeons and Dragons, fighting is synonymous with combat. And the only rules for combat in D&D are those related to physical combat, in chapter 9 of the PHB (unlike some unrelated game systems, which also have rules for social combat). Looking at page 189, the first page of Chapter 9, we see when combat starts under The Order of Combat.

The order of turns is determined at the beginning of a combat encounter, when everyone rolls initiative.

Thus combat, or the fighting, starts when we roll initiative. When does it end? The next sentence says

the fight continues to the next round if neither side has defeated the other.

The Combat Step by Step sidebar also says

Repeat step 4 [Take turns] until the fighting stops.

So we can reasonably conclude that the fighting ends when the characters involved in the combat stop fighting, either by being defeated or by choosing to lay down their arms. This is the natural definition of stopping fighting. At this point, the DM normally stops counting rounds unless there is some other time-sensitive issue to be resolved.

However, there is some wriggle-room. Most spells don't simply ask if a creature is 'fighting'. Rather, they are conditioned on a creature fighting some other creature. This is more ambiguous. Obviously, if one creature is using their actions to harm another creature, they are fighting, but there are numerous circumstances where the line can be fuzzy. What if a creature switches sides half-way through combat? What about creatures who are lingering by the side-lines? What about a person who is buffing their allies but who isn't using any combat abilities? In these instances, the DM needs to use common sense to adjudicate the situation, because such circumstances are too complex to be covered by some blanket rule.