It looks like nothing happens - a program is launched and shuts down right after the start, no error messages etc.
Battle viewer requires Microsoft Visual C++ 2015 Redistributable installed. Without it, the viewer can't be launched. But the viewer can also act like that on several devices even with the system component installed.

What to do:

1. Renaming the file vcruntime140.dll
   Open the local game files in Steam. There are several folders named battle_client_*** - battle clients for different worlds with different battle systems versions. The most common was battle_client_new (at the moment this guide was compiled).
   In the client folder, find the file vcruntime140.dll. Rename it, e.g. old_vcruntime140.dll, then try to relaunch a battle replay or simulation. If it doesn't work (and window behaviour remains the same), move to the next step.
   
   
2. Reinstall the Microsoft Visual C++ 2015 Redistributable
   The system component might be not installed or corrupted. Reinstallation or restoring might help - the installation file can be found in the local game files, subdirectory \_CommonRedist\vcredist\2015, or download it from Microsoft website.

The viewer starts, loads a battle, then shuts down with a system alert.

In the local game files find the folder with battle client used last - folders are named battle_client_***, the used one can be found by the latest change time and date. Find the log.txt file.
Open it, copy and then send us via new community thread (or already existing one about watching problems). Please tell the exact video card model, total RAM amount, OS version (and also is it 32 or 64 bit) .
If there's a specific battle that doesn't work (all the others work correctly), or the problem is with simulation, tell us the name of your game account and where was the battle (in case the problem is with a battle), or all simulation parameters.

It might be that, for some reasons, the connection with battle server is rejected. Try to watch the replay a bit later, but still it's better to report via community threads or in-game support.

Like said before, start a new community thread (or join an already existing one about watching problems). Please tell the exact video card model, total RAM amount, OS version (and also is it 32 or 64 bit) .
If there's a specific battle that doesn't work (all the others work correctly), or the problem is with simulation, tell us the name of your game account and where was the battle (in case the problem is with a battle), or all simulation parameters.

Also, follow this if there're problems with simulations only, or ongoing battles only with working replays and simulations, etc.