See also the official documentation:
Help Center > Group Owners Manual > Managing group topics and messages

Message Moderation

When Groups.io receives a message intended for a given group it makes a series of evaluations to decide whether that message should be accepted immediately into the group's Messages section or whether it should be delivered instead to the Pending page so that a group moderator or owner can determine whether to accept or reject the message. The latter is referred to as Message Moderation.

Note: although there are many rules, the default for (almost) all of them is not to cause a message to be moderated — a group admin must enable each rule before it applies to any messages.

An exception is New Members Moderated, which is the default Spam Control setting when a group is created.

The message moderation rules are applied equally whether the message is created online in the group's web pages (New Topic and Reply features) or is sent to the group by email. Messages are forwarded to members by email at the same time that they are accepted into the group's Messages section.

Message moderation in Groups.io is very flexible, including controls for moderating messages at the group, hashtag, topic, and individual member level. This flexibility reflects the understanding that there is no one "right" way to moderate messages in a group - different groups have different needs.

FAQ

I just started a group, how does moderation work?

When you create a new group at Groups.io the default Spam Control setting is New Members Moderated. In part this reflects the fact that one of the primary purposes of message moderation can be to prevent people from using your group to distribute spam, or any other undesired material, to your group's members. When a message is subject to moderation it is delivered to the Pending page so that a group owner or moderator can decide what to do with the message.

In this context "new" does not refer to how long the person has been a member, but rather how many messages of theirs have been accepted by moderators. Together with New Members Moderated goes the Unmoderate After setting. By default that is set to one, so if a message of theirs is approved, their subsequent messages will not require moderation.

How do I know who is specifically moderated?

In the members list there may be badges after the display of each member's email address; some badges relate to moderation and when present these indicate that the member has an override to the group's Moderated checkbox. See Status Badges in the Members List for a list of the badges. In a new group, the NMM (New Member Moderated) is the only moderation badge that is likely to appear, all of the rest must be manually assigned to the member by a group owner or moderator.

Note: particularly long email addresses my cause badges to be hidden by the next column (Delivery). in such cases you may need to widen the display window, or zoom out, to make the badges visible.

Each member's Posting Privilege setting may override the group's Moderated checkbox. See the Member Controls and Group Controls sections below for more detail.

How do I approve or reject pending messages?

If you received a Message Approval Needed notification there will be a copy of the pending message attached. You can approve the pending message by replying to the notice, or you can approve, reject, or delete the message by following the instructions in the notice. You can also follow a link in the notice to see the notice in the list of pending messages on the group's Pending page.

If you're looking at the pending messages on the group's Pending page you can act on them singly or in groups by using the checkmarks and buttons in the list, or you can open each to read it and act on it.

See How to Handle Pending Messages for details.

How do I unmoderate everyone?

See https://groups.io/g/GroupManagersForum/message/18347.

How do I unmoderate a single member?

See https://groups.io/g/GroupManagersForum/message/18352. 

Group Controls

The group controls are found on the group's Settings page:

The Spam Control section of a that page contains two checkboxes relevant to message moderation.

Moderation (changed Jan 15, 2020): This is where you choose if and how the group is moderated.  The choices are "Not moderated", "All messages are moderated", and "Messages that start new topics are moderated".

New Members Moderated: This checkbox causes newly joined members to start with the Override: new member moderated. If unchecked new members start set to Use Group Moderation Setting.

Unmoderate After: This selection controls how many messages from a member must be approved before that member is no longer considered "New".

The Message Policies section has a few more related controls:

Allow Nonmembers to Post: This checkbox allows the group to receive messages by email from non-members, but all such messages will be moderated (overriding the Moderated checkbox).

Automatically Moderate Topics Older Than x days: This checkbox causes topic moderation to be automatically turned on when each topic reaches the specified age (overriding the Moderated checkbox).

Viruses: This control allows detection of a virus in an incoming message to cause the message to be moderated (overriding the Moderated checkbox) instead of blocked.

The Message Formatting section (surprisingly) has one more related control:

Attachments: This control allows a message with one or more attachments to be moderated (overriding the Moderated checkbox).

Be sure to Update Group to save changes to settings.

Member Controls

See also: Moderating an Individual Member

Posting Privileges: this section at the bottom of a member's page, accessed from the Members list, has a multiple-choice selection ("radio" control) that directly controls how messages from this member are handled:

Use Group Moderation Setting: This makes the member's messages subject to the various group settings (above), and to topic moderation.

Override: not moderated: Messages from members with this posting privilege are allowed to post without requiring approval, without regard to the group's Moderated setting.

Override: moderated: Messages from members with this posting privilege are held in the group's pending list, without regard to the group's Moderated setting.

Override: new member moderated: If the group's New Members Moderated checkbox is checked an Unmoderate After option is available. That sets the number of messages approvals required to remove this override from a membership address. This count is displayed in a dark grey badge adjacent to the NMM badge (see above).

Messages from members with this posting privilege are held in the group's pending list, without regard to the group's Moderated setting. Each time a moderator approves a message form this address that number is reduced by one; if the message is rejected or deleted the count retains its current value. When the count for this address reaches zero the New Member Moderate override is removed from this address and it is set to Use Group Moderation Setting instead.  This choice may be reinstated any time you feel that it's needed.

Override: not allowed to post: Messages from members with this posting privilege are rejected, without regard to the group's Moderated setting.

Override: moderate the first message of every topic this person starts: A message from a member with this posting privilege is held in the group's pending list if that message starts a new topic. This would be the case if the member used the New Topic button in the group, or if the member created a message with new Subject text in their email interface.

Override: moderate all messages of every topic this person starts: All messages, from any member, are held in the group's pending list if that message is a reply to a topic started by a member with this posting privilege (or is the message that started such a topic).

Integration Controls

Integrations: while not members, Integrations allow third-party services and nonmembers to send messages to the group. Each integration has a Moderated checkbox to cause messages from this source to be moderated (overriding the group moderation controls).

Topic and Hashtag controls

Topic Options: These controls are available (to a group admin) via the More menu that appears in the bar below each message.

• Moderate Topic — all replies to this topic will be moderated
• Lock Topic — all replies to this topic will be rejected.

Hashtag Options: These controls are available (to a group admin) via the Edit button that appears on each Hashtag on the Hashtags page or when using the Create Hashtag function at the bottom of that page. Hashtags apply to any topic containing that Hashtag in its Subject line.

• Topic Duration w/ Lock Topic —Topic will be locked after the specified time period.
  
• Moderated — Messages (New Topic or Reply) will be moderated.
  
• Replies Unmoderated — Replies to this topic will bypass the group's Moderated checkbox.
• Locked — Replies to this topic will be rejected.
• Use by Mods Only — Messages (New Topic or Reply) will be rejected unless posted by a group admin.

How to moderate - details

See this wiki page:  How to handle pending messages