If you find that sometimes calendar invitations go missing, this might help.
I manage my emails and calendar etc with Google’s Gmail/Calendar/Contacts. But I use Apple devices (MacBook, iPhone, iPad). This works really well, but very occasionally I found I would miss a calendar invitation. The organiser would apologise profusely for missing me off the circulation, and then check and find out that they hadn’t made a mistake at all. I was on the recipient list, but I hadn’t received the email.
It turns out that Apple is trying to be helpful. The sender is sending the invitation from their iCloud calendar, and Apple’s system sees that I have a an iCloud account so it sends it directly to the iCloud calendar application. The event is visible in the Apple Calendar which I, of course, don’t use on my MacBook and don’t have visible on my devices.
The fix is to login to iCloud, go to the Calendar, and delve deep into the preferences to tell Apple to send you invitations by email. See the images below for a step-by-step guide.
Login to iCloud.com and click on the Calendar icon 
In iCloud Calendar click on the cog icon in the bottom left corner 
Choose Preferences from the menu that pops up 
Select the Advanced tab at the top 
Where it says ‘Invitations’ at the bottom, if ‘In-app notifications’ is selected…. 
…change it so that it sends you an email, then click Save