HVAC Fan Running

I ordered a new stat. The one we have was acting up last winter. We use the programming feature for the heat, and it wouldn't start on its own on a Monday morning. lol After a little help, it ran fine all week, and weekend. The ac, it's either on or off.
My wife likes the stat called, "The Nest", so one is on the way. My step-daughter has one and likes it.