If you're interested in pursuing your glorious rewards, the best place to find yourself is in rated pvp, as each win will award you around 25-100, depending on the bracket, with the first of each day in each bracket being doubled for participating in that type of content. As a result, doing every bracket you can is highly recommended. Outside of this there are 1-time Quests available from the same area as the Weekly Zone Quests, simply asking to Kill a single player of the opposite faction, which rewards 50 points of conquest.
There is a reward players can get regardless of ranked, by filling the Weekly Conquest Cap. If you do not fill the cap one week, you can earn the item the week after, and your progress bar will not reset.
Conquest points previously were a source of "advanced" currency from primarily rated PvP activities, and used as a way to target specific pieces of gear with the caveat of specific rating requirements necessary for items of high significance, such as Weapons and Mainset pieces (way back when).Keeping with that theme, you do still earn conquest with that regard, but the need to find a vendor and worry about how you will obtain specific pieces has been taken care of, as now the Progression Bar above your Group Finder/PvP tab now lists specifically how much you have, and how much you've got until you will receive your next reward(s). For example, the first level of conquest requires 500 earned to receive your 445 weapon, giving all specs something to go after.
Participation for rewards used to be a seemingly rewards-focused or 'Checklist' style, where if you'd already earned your daily or weekly goal for the week, or perhaps the Limit of conquest points during the time in which it was a currency, you had nothing else to play for but rating. This is being thrown out for a system that rewards those who play, as the conquest "limit" is not there***, and as long as you keep playing, you will earn your rewards in due time. For those who are limited on time, there remains a way to gain additional rewards for/based on weekly performance, in the form of the War Chest. These can be found in the PvP hub areas of either the Dueler's Guild of Boralus or Mugambala in Zandalar. The rewards for this are similar in regards to the Mythic+ chest system, where earning Conquest points will (at the end of each week) give a reward in the chest the following week. The game will always choose the highest bracket That you have played games in for the week when deciding what rewards you're eligible to earn.
Previously, with the old system, there was either limits to the quantities of points earned, or Limiting of specific pieces of gear behind ratings. In the Honor 3.0 system, conquest earned will give gear for each slot regardless (in a linear sequence), and following the completion of a set, will then earn higher item levels of similar pieces of gear, such as a 440 vs a 460+ piece. In obtaining a higher rating, The gear reward Ilevel will go up at a linear rate as well.
Once a week from the same location as the War Chest, you'll find a quest from either Grand Marshal Tremblade or High Warlord Volrath to kill 10 enemy faction members in a specific zone for that week. Doing so will earn you some conquest as well, similar in reward quality to the War Supply Chest. In addition, The Arena Calls will also award conquest as well, in the event that it's the weekly event for it, so pay attention to your calendar, as it could be well worth your while to do a few skirmishes.
By popular demand, there's been several requests to have a map of the spawn locales, as the chests are always in a set pattern of potential locations, so it would obviously help to know where those are
With the change to arenas becoming a tier system, Gladiator has also changed. Now, to obtain the Gladiator title you need to win 50 games while on the Elite bracket. However, the Dread Gladiator title and other rank 1 titles for example still have the same criteria as Legion and previous expansions, requiring the player to place in the top 0.1% of his faction. Dread Gladiator's Proto-Drake requires 50 wins while in the Season 1 Gladiator bracket.
Similar to how gear is handled in Mythic+, once you successfully complete Matches or Objectives in either Rated, or World PVP, you may find yourself with pieces of the Dread Aspirant Alliance Leather or other armor-specialized Dread Aspirant setpeice gear being awarded to you randomly. These pieces can also drop out of/from the Supply chests, and bounty bags, in addition to being also randomly awarded from completing skirmishes and unrated pvp. For those solely wishing to obtain the appearance, but maybe don't wish to engage in PvP, These and other similar appearances are usually obtainable for a (number of) Mark of Honor, most likely near the Profession-recipe vendor in your faction's PvP hub.