The fridge-door chore chart works for about a fortnight. Then it's out of date, nobody remembers whose week it was for the bins, and the person who keeps the house running ends up doing the reminding as well as the chores. What actually helps is small: every chore has someone it belongs to and a day it's due, and finishing it is visible to everyone.
Here a household of up to six people shares a chore list, while each person keeps their own to-do list private. Give a chore to someone in the household, to a child who doesn't have an account (you add them by nickname), or to Anyone for the jobs whoever gets there first can do. Each chore shows in the To-Do of the person it's for, on its due date. Anyone can tick it off and everyone sees who did, and a Household view lists what's open for each person. Whoever creates the household needs a Premium plan and every other member needs Basic or higher; the to-do list on its own is free. For just the two of you, see the shared to-do list for couples.