Email follow-ups, and jobs slipping through the cracks

How do you handle multiple micro-tasks, being either 1/ delegated or 2/ waiting on somebody else, without constantly keeping them into your face, but making sure things don't slip through the cracks?

My team tried different tools but ended up building an internal tool for email that frankly is 80% of what we use to communicate and follow up on things that do not go in Jira.