From Advanced Options, navigate to the Log - Publish tab.

From this table, you can view the status of all past and current publishing logs.

Publish Execution Log Fields

Column Name	Description
Global ID	The global ID for this log entry.
Entity	The global ID for the entity being published. A foreign key on Publish Entities.
Status	Defines the status of this entry amongst (QUEUED, RUNNING, COMPLETE, and FAILED).
Timestamp	The timestamp for the log entry.