You can see all the tasks that are assigned to you by going to the "Tasks" page.
The "Tasks" page show all the tasks that are assigned to you or where you are one of the assignee, except the tasks that are marked done. There are four lists:
Task "start date" is not used in the "Tasks" page.
You can also see your teammates tasks from the same place. Click on the filtering drop down on the left side and choose a person.
Don't worry about your private projects and tasks because you can only see the tasks from the projects that you are invited to.