I have mentioned how to download the eventlog.xml file to view the events which are happening on your Azure App Service (Web App, Mobile App, API App, Logic App) here and here. You can also look at the event logs in a event viewer using KUDU, I discussed KUDU here. Keep in mind that if you are running multiple instances, that you are viewing the event logs for a single instance only.
To access the event logs using KUDU, after login in select Support from the Tools menu as shown in Figure 1.
Figure 1, view event logs in KUDU
Once the Support page renders, click on the Analyze link, then Event Viewer, as shown in Figure 2.
Figure 3, Azure App Service Event Viewer details