It's important to monitor systems for any suspicious activity and to detect any performance issues. API Gateway, DynamoDB, and Lambda functions all support CloudTrail, CloudWatch, and X-Ray for monitoring and alerting. They are discussed as follows:

• CloudTrail allows you to monitor all APIs and access to resources by any user or system.
• CloudWatch allows you to collect and track metrics and monitor log files, set specific alarms, and automatically react to changes in your AWS resources.
• X-Ray is a new service that traces requests and can generate service Maps.

The combination of these free systems gives you very good insight, out of the box, into your serverless system.