Hiding - DEFINITIVE

For this campaign, I would submit the following items for consideration:

Hide (Action from the PHB)

When you take the Hide action, you make a Dexterity (Stealth) check in an attempt to hide, following the rules for hiding. If you succeed, you gain certain benefits, as described in the "Unseen Attackers and Targets" section later in this chapter.

Unseen Attackers and Targets (in Combat chapter from the PHB)

Combatants often try to escape their foes' notice by hiding, casting the invisibility spell, or lurking in darkness. When you attack a target that you can't see, you have disadvantage on the attack roll. This is true whether you're guessing the target's location or you're targeting a creature you can hear but not see. If the target isn't in the location you targeted, you automatically miss, but the DM typically just says that the attack missed, not whether you guessed the target's location correctly.  When a creature can't see you, you have advantage on attack rolls against it.  If you are hidden — both unseen and unheard — when you make an attack, you give away your location when the attack hits or misses.

Hiding (From D&D Beyond- Updated)

The DM decides when circumstances are appropriate for hiding. (this sentence does NOT appear on page 177 of the PHB where the rest of this section does, but it has become official in the update on DDB) When you try to hide, make a Dexterity (Stealth) check. Until you are discovered or you stop hiding, that check's total is contested by the Wisdom (Perception) check of any creature that actively searches for signs of your presence.  You can't hide from a creature that can see you clearly, and you give away your position if you make noise, such as shouting a warning or knocking over a vase. An invisible creature can always try to hide. Signs of its passage might still be noticed, and it does have to stay quiet.  In combat, most creatures stay alert for signs of danger all around, so if you come out of hiding and approach a creature, it usually sees you. However, under certain circumstances, the DM might allow you to stay hidden as you approach a creature that is distracted, allowing you to gain advantage on an attack roll before you are seen. (emphasis mine)
Passive Perception. When you hide, there's a chance someone will notice you even if they aren't searching. To determine whether such a creature notices you, the DM compares your Dexterity (Stealth) check with that creature's passive Wisdom (Perception) score, which equals 10 + the creature's Wisdom modifier, as well as any other bonuses or penalties. If the creature has advantage, add 5. For disadvantage, subtract 5. For example, if a 1st-level character (with a proficiency bonus of +2) has a Wisdom of 15 (a +2 modifier) and proficiency in Perception, he or she has a passive Wisdom (Perception) of 14.
What Can You See? One of the main factors in determining whether you can find a hidden creature or object is how well you can see in an area, which might be lightly or heavily obscured as explained in chapter 8, “Adventuring.”

Vision and Light (in Adventuring Chapter from the PHB)

The most fundamental tasks of adventuring--noticing danger, finding hidden objects, hitting an enemy in combat, and targeting a spell, to name just a few--rely heavily on a character's ability to see. Darkness and other effects that obscure vision can prove a significant hindrance. A given area might be lightly or heavily obscured. In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight.  A heavily obscured area--such as darkness, opaque fog, or dense foliage--blocks vision entirely. A creature effectively suffers from the blinded condition when trying to see something in that area.
The presence or absence of light in an environment creates three categories of illumination: bright light, dim light, and darkness.
Bright light lets most creatures see normally. Even gloomy days provide bright light, as do torches, lanterns, fires, and other sources of illumination within a specific radius.
Dim light, also called shadows, creates a lightly obscured area. An area of dim light is usually a boundary between a source of bright light, such as a torch, and surrounding darkness. The soft light of twilight and dawn also counts as dim light. A particularly brilliant full moon might bathe the land in dim light.
Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of an unlit dungeon or a subterranean vault, or in an area of magical darkness. 
Darkness creates a heavily obscured area. Characters face darkness outdoors at night (even most moonlit nights), within the confines of an unlit dungeon or a subterranean vault, or in an area of magical darkness.

So what does this all mean?

Practically speaking, the only time that a character can hide is an an area that is lightly-obscured or heavily-obscured.  Additionally, during combat, you must break, not only sight, but all perception. Here are the practical options for players:

Hide as an action (or bonus action for rogues)

If a character meets the conditions for hiding, that player may use an action to roll a stealth check that will be opposed by the passive perception of any creatures who may be able to perceive the character.  The character stays hidden until an enemy perceives them or until they take an action that would void their stealth roll, such as attack, use an item, communicate with their party members, etc.

Make a melee attack while hidden

Players who have successfully hidden, and made a stealth check, are permitted to make a melee attack roll while remaining hidden provided they do not violate the condition that granted them that hidden condition.  For example, if a rogue goes behind a large rock and hides, that rogue cannot come back out from behind that rock, move fifteen feet and attack a target while remaining hidden.  In combat, and in most situations, a hidden character emerging from an area of broken sight will give that character's position away.

Make a range attack while hidden

Players who have successfully hidden, and made a stealth check, are permitted to make a range attack roll while remaining hidden, however, simply breaking line of sight is not enough to conceal the characters position.  For example, if a rogue sneaks behind a tree that is only large enough to conceal that rogue in one way from an opponent, that opponent still knows exactly where the rogue is, regardless of a hide check.  There must be a reasonable repositioning or movement by the hidden character that is not as simple as ducking behind a barrel.