One key element between serverless components is messaging. Amazon SNS is a fully managed pub/sub messaging for distributed or serverless applications. There is the option from one to many messages to push out. E.g. a publisher places a message in a topic and all subscribers get a copy of the message. You can use the message as a trigger for a Lambda function, the message could be send to a message queues from which a cluster is consuming inbound messages or I can even push a message to a ticketing system HTTP/S like Jira or Redmine to mention a few I am using. SNS helps to push things through.
An other way to make content delivery faster is Amazon CloudFront in Edge Locations. You can accelerate on different areas across the globe, outbound and inbound content transfer to different regions, e.g. easy to store via a S3 bucket.
Over 100 Edge location around the world could be used to improve performance and fetch the content, if the nearby cache do not provide the required content as shown above. This example shows one form of caching in Edge Locations.