You can always see DNA matches for your own DNA kit. Additionally, you can see the DNA matches for any DNA kit you activated and manage in your own account.
If your DNA kit was activated and is managed through another person's account, that individual will have access to view your DNA matches as well.
For DNA kits that you manage, you have the option to share DNA matches with others using the "Share DNA results" feature. Please click here to learn more about this functionality.
DNA Matching is enabled by default on your family site, allowing those who share DNA with you to view the DNA matches you both have in common.
For additional details about privacy options for your DNA data and DNA matches, you can find more information here.