Posted Below Without Content Spoilers.
General Tip: Right-clicking on any creature including your player will give you more information. It is good to do often, especially as you gain more knowledge of different abilities and effects by playing more classes and taking part in the community.
VERY IMPORTANT NOTES:
Definitions:
1. a) "Chests": if can walk onto its tile without using a turn to open it first and THEN it asks you whether you want to open it it is a "chest" even if it looks different;
b) "Vault Doors": Doors that ask for confirmation are always Vault Doors, although there are different types of "Vault Doors" that are functionally identical but look different, such as rocks;
FOCUS: Saying Yes to Opening a Chest or Door - anything that asks for confirmation whether you want to open it - is a Bad Idea!!!
READ!!! CAN END YOUR RUN!!!
(there MAY be some exceptions that are required to win a campaign, but it is an excellent idea to ask in the in-game chat (usually quickest) or on this Steam forum or the main "forums.te4.org" web-site beforehand (remember the game is turn-based - enemies don't move or act until you do

If you state in in-game chat your area or dungeon name and game difficulty including permadeath setting (and lives left if on Adventure) you can get an idea whether it is worth risking it. Generally though if you don't have any lives left it's not a good idea to risk super powerful monsters appearing. Your race/class and your level is accessible by mousing over your player name in-game - (if asking on a forum mention these too) - just be aware that any enemies that were still alive when you died will have full health and no statuses or effects. However the final decision is always up to you.

REASONS YOU MIGHT WANT TO CONSIDER OPENING A CHEST OR VAULT DOOR:
2. a) You have a fair number of games under your belt, and being a tough melee class certainly helps (Rogues are not a good idea at low levels because they start out squishy due especially due to low relative HP);
b) You're in a Location/Dungeon you CAN revisit and CURRENTLY NOT ON ROGUELIKE PERMADEATH MODE and You Are NOT On Your Last Life:
(i) You CANNOT revisit One-off locations (for info on these see below - the story in this post already talks about the first one

- You will need to weigh your chances of doing so (including how many lives you have left if any) and whether risk/reward is a good tradeoff;
c) And even then certain zones such as Dreadfall are not worth the risk/reward to open chests or vaults for experienced players and even more so for newer players because their regular enemies are so tough!
NEW AND EARLY PLAYERS:
If you are a new player or a squishy class (generally all ranged and magic classes are relatively squishy compared to melee classes, but you will found out any exceptions from play and interaction with the community via in-game chat or forums):
WHAT MAKES CHESTS AND VAULTS SO DANGEROUS:
3. What makes chests, or any other tile or door that asks for confirmation before you open them, so dangerous is:
a) if/WHEN they generate an enemy or enemies or allow enemies out;
b) (i) Chests and other 1-tile non-doors that ask for confirmation are "if" but it only takes one bad chest result to end a run!;
(ii) Vaults are practically guaranteed to have powerful enemies and lots of them too;
(iii) Chests and vault enemies are always a lot tougher due to higher level than the regular enemies in the zone and higher chances of being rare or unique with one or more classes;
(iv) Chests, although they don't generally have as many (and sometimes no) enemies, they have the added lethality that any monsters start out next to or around you when you open the chest (they "appear" or "pop out").
SPOILERS ABOUT AGE OF ASCENDANCY CAMPAIGN (AoA) ONE-OFF LOCATIONS ON MAIN ToME/TE4 FORUM