Kudu is an open source (https://github.com/projectkudu/kudu) engine, which powers Azure website Git deployments and continuous deployments on all Azure websites. There is a Kudu service in every website, which can be accessed via the following URL https://mysite.scm.azurewebsites.net. If you have a custom domain name implemented, you will need to use the azurewebsites.net endpoint unless you do extra DNS configuration for this endpoint.

The Kudu service website looks like this:

There are some useful tools in here for working with logs; the Diagnostic Console (under Debug Console) has a CMD and PowerShell console in the browser along with a directory explorer, which allows you to work with logfiles:

You can get more information on the Kudu service at https://github.com/projectkudu/kudu/wiki/Accessing-the-kudu-service.