There are a couple reasons why your event may not show up on your website.
Your event is not set to active.
Your event category is not set to active.
The publish date on the event's settings tab is set to a future date.
Your Event is Not Set to Active
You can make your event active by going to the event itself and toggling the inactive/active button.
The other way is to go to the events dashboard. This shows you a list of all upcoming events. You can toggle multiple events from inactive to active at one time.
Your Event Category is Not Set to Active
If your event is set to "Active" but isn't showing up on the front-end, go to the Details tab of the event and check which Category it is assigned to.
Then go to Event > Categories on the backend and check to see if the event category is active. If the category for your event is inactive, toggle the category to active.
The Publish Date is Set to a Future Date
If your event is set to "Active" but isn't showing up on the front-end, go to the event and visit the Settings tab. Change the Publish Date to today's date.
