AWS Lambda functions can be monitored by collecting and visualizing JSON request and response payloads using Datadog. This helps identify the root causes of function failures, such as misconfigured requests or code issues within the function itself. Datadog also provides the option to scrub sensitive data from collected payloads. Additionally, tracing serverless applications with Datadog allows for quicker troubleshooting by tagging spans that represent function invocations with relevant payload data. Payload ingestion is currently available for Python and Node.js runtimes and can be enabled by adding the environment variable DD_CAPTURE_LAMBDA_PAYLOAD to Lambda functions and setting it to true.