Stardew Valley 1.3.x is an upcoming release that includes multiplayer support and new content. Beta versions were posted to the Steam beta channel starting 30 April 2018 (1.3.3) and to the GOG beta channel starting 04 May 2018 (1.3.8).
Overall changes

This is an incomplete list of changes between 1.2.33 and the 1.3.x release.

Changes

Added support for multiplayer over GOG, Steam, or LAN.
Added multiplayer chat feature.
New content:
Added Night Market event.
Added Abigail encounters as you descend in the mines.
Added new NPC dialog.

Ongoing beta

1.3.16 (05 June 2018)

Fixed 'introductions' quest tracking the wrong number of villagers for farmhands.
Fixed cabin fridges emptying when host reloads.
Fixed Secret Santa assignments changing.
Fixed items missing from festival shops when playing in Chinese.
Fixed traded fishing tackle breaking after one use.
Fixed tree seeds not being harvestable in multiplayer.
Fixed spouse position issues.
Fixed players stuck in wall after Emily's 10-heart event.
Fixed wallpapers/floors vanishing and resetting.
Fixed spawned mine ladders/shafts not being synced correctly in multiplayer.
Fixed slimes aggroing player during secret woods event.
Fixed horses becomes unmountable after entering a new location.
Fixed horses vanishing when warping between two quickly.

1.3.15 (30 May 2018)

Break-up event is now less harsh.
Fixed issue where farmhands only saw the first Junimo bundles page when accessed outside of the community center.
Fixed crash upon returning to a level of the mines with a chest, after having just been in it.
Fixed machines sometimes breaking when you're near torches.
Fixed crash when attempting to load a quest that hasn't been localized yet.
Fixed monster cries being heard outside of the mines.

1.3.14 (25 May 2018)

Added a quest to hint at the magnifying lens.
Re-enabled moving & demolishing buildings in multiplayer (although only the host can do it).
Fixed bug allowing players to spawn a staircase on the bottom mine level.
Fixed mermaid show not playing if volume is muted.
Fixed crash when selling many items to Pierre or through the shipping bin.

1.3.13 (24 May 2018)

Added separate chests in the mines for each player.
Fixed controls locking up in Stardew Valley Fair fishing tent.
Fixed duplicate cursors in minigames.
Fixed crashes buying furniture.
Fixed freezes when fishing during events.
Fixed crash caused by ordering a building construction the day before a festival.
Fixed crash breaking certain objects in the skull cavern.
Fixed horse-related bugs with movement between screens/clipping.

1.3.12 (22 May 2018)

Fixed all players seeing milking messages.
Fixed object desync on farm between players.
Fixed lighting issue in spa.
Fixed clocks becoming de-synced from server latency (now will disconnect player).
Fixed high network usage when NPCs moving.
Fixed delay when using bombs.
Fixed hidden mines ladder to skull cavern.
Fixed erroneous thunderstorm weather forecast in summer.

1.3.11 (16 May 2018)

Fixed beds regenerating energy in single player.
Fixed bomb framerate/delay issues (testing some).
Fixed farmhand crash when junimo is out at the farm.
Fixed inability to use emojis while chatting when menu was up.
Fixed fishing tackle breaking after one use.
Fixed Winter 8 festival overwriting first item when playing in Chinese.
Fixed forgetting level ups when disconnected.
Fixed lost stardrop stamina after disconnect.
Fixed crafting recipes vanishing when disconnected.
Fixed non-slime monsters being tracked in "Initiation" quest.
Fixed quests breaking or not tracking properly when disconnected.
Fixed weather report always sunny after reload.

1.3.10 (09 May 2018)

Fixed only LAN option being available at join screen.
Fixed torch & debris related lag issues.
Fixed crash after upgrading the community center.
Fixed object at (0, 0) causing machines to be destroyed when harvesting (thanks @MysticTempest!).
Fixed forage items spawning in inaccessible places.
Fixed travelling cart 'out of stock' message.
Fixed inability to get coffee at Night Market.
Fixed crashes related to Invisible Doors.
Fixed unable to reassign farm animals to other buildings.
Fixed startup_preferences permission crash.
Fixed objects pulse briefly when player enters map.
Fixed town map graphic inconsistencies with festivals.
Fixed treasure chests not appearing every 10 levels in mines.
Fixed spouse disappearing.
Fixed blocked path for secret note 20.
Fixed obsolescence of secret note 20 after purchasing "community upgrade".
Fixed slimes not applying "slimed" debuff.
Fixed freeze if all players are not in bed by 2am.

1.3.9 (04 May 2018)

Visual C++ redistributable update to partially fix the "LAN Only" connection issue.
Fixed furniture/wallpaper/flooring getting removed from sheds.
Fixed crash when interacting with farm animals left outside