Sometimes, connections between Zapier and the apps you use break. Usually Zapier warns you about this, but sometimes not.
To check, goto the My Apps page and see if any of your apps are marked as "Disconnected". If so, follow the prompts to reset them.
From that page, you'll also be able to click on the elipses (...) beside each app an manually test the connection. If it reports back broken, you'll be able to fix it.
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Sometimes zaps just stop working, and the act of switching them on and off again, will cause them to work again - or also prompts Zapier to test the connections of each app in the zap and report any potential problems.
Some apps trigger immediately, others are known as polling triggers meaning Zapier will check for new data once every 1, 2 or 15 minutes depending on your plan level. If you're seeing a trigger delay, this may be why.
If your zap is triggered by a webhook step, or if the trigger app gave you a URL when you were setting up, make sure you've added this correctly inside the app. If it's not correctly set the app won't be able to send data to Zapier correctly, and your zap won't trigger.