Activity Timeline (Lightning) 

The Activity Timeline is a new feature of lightning. It shows you all of the activities (emails, notes, calls, and events) associated to the account by date. The activity timeline shows each activity with their particular icon and you can open each type by clicking the down arrow to read what you need. You also have the option to Expand all so everything in the timeline is open.

Look and feel video!

Activity Timeline Filter

Can't find the email you're looking for? Check your Activity timeline filter to see how far back your timeline is going. Check the video above or the image below! Click the Filter icon to open options to change the date range, types of activities, and type. 

Activity history (Classic)

The Activity History (Classic) and the Activity Timeline (Lightning) view are two different views, and behave differently.

Activity History:

This read-only object is displayed in a related list of closed activities—past events and closed tasks—related to an object. It includes activities for all contacts related to the object. 

Why Activity Timeline is stronger: 

Activity History only allowed you to read emails and it required you to open up each email into a different tab. There was no way to really understand the subject and you can't view all the notes you might have had inbetween. This was only an email history, not a full history of your relationship with the account. The timeline gives you this view simply and easily.