@Nikks, by default all logs are in  %ProgramData%\Veeam\Backup\ 

In thath path you can check various folders jobs related 

Thanks Andanet. But there are many log files inside the folders. Any specific log files to check for example replication?

In that folder there are job folders so if you have a replication job then check that subfolder.  Each job has a folder and then main components are in the root directory.

Sorry @Nikks but I'm replying from my smartphone and not remember all folders name but as wrote @Chris.Childerhose you can check one folder for every job, a folder for the restore and so on. 

Hoi @Nikks, as @Andanet and @Chris.Childerhose mentioned, you will find all required logs there.
Under the following link, you will get informations from the User Guide: Managing Logs - User Guide for VMware vSphere (veeam.com)

So for example, when your Replication Job ist called “Example-Replication” - you will find your logs under %ProgramData%\Veeam\Backup\Example-Replication\

Regarding your question on a specific tool: i don’t know if the Support Team from Veeam have special tools, mostly i am using Notepad++, VeeamONE can also give some insights if you have trouble. In the past i’ve often used BareTail - a free windows log-file tool with real-time filtering, maybe also an option for you.

As someone from support I can say we don’t use a specific tool. It’s just notepad ++ and sublime (I’m a sublime guy, but notepad++ is awesome too).

%ProgramData% & Notepad++ is the usual. Alternatively, use the log collection wizard and dig into the zip file it produces. 

Both of these are my go-to as well for logs.

TIL.  I guess I’ll have to look into this...looks pretty cool at first glance.