In Lightning, activities can be configured as Activity Timeline or Related Lists. As an admin, you can configure this from Setup | User Interface | Record Page Settings | Default Activities View (desktop only).
However, users also able to personalize the activities view on their own as Activity Timeline or Related Lists from Settings | Display & Layout | Record Page Settings.
Another thing that admin can configure is to enable roll-up activities to a contact's primary account, this means activities (event, task, and email) links to Contact will appear in their direct Account too. To configure this, navigate to Setup | Feature Settings | Sales | Activity Settings, enable roll up activities to a contact's primary account.
Additionally, activities (event, task, and email) in Opportunity and child objects (with Master-Detail relationship to Account only) will appear in Account too, this behaviour is applicable for both views with Activity Timeline or Related Lists. However, Case activities will NOT roll-up to Account.