I can query my Seat table for all seats where there is no invite assigned:

seats = Seat.query.filter_by(invite=None).all()

However, when querying for all seats that have an invite assigned, I get a NameError:

seats = Seat.query.filter_by(invite!=None).all()

NameError: name 'invite' is not defined

Here is my Seat class:

class Seat(db.Model):
    id = db.Column(db.Integer, primary_key=True)

    invite_id = db.Column(db.Integer, db.ForeignKey('invite.id'))
    invite = db.relationship('Invite',
        backref=db.backref('folks', lazy='dynamic'))

How can I query for all seats where the owner is not blank?

The filter_by() method takes a sequence of keyword arguments, so you always have to use = with it.

You want to use the filter() method which allows for !=:

seats = Seat.query.filter(Seat.invite != None).all()