Datadog integrates with Cloud Run to collect and visualize key metrics, traces, and logs. To set up the integration, service account impersonation is required, along with enabling specific APIs and ensuring that projects are not configured as scoping projects. Datadog offers a sidecar container methodology for instrumenting Cloud Run applications, which can also be done through Dockerfiles or buildpacks using lightweight tools like `serverless-init` and `datadog-init`. The integration provides an out-of-the-box dashboard with key metrics such as serverless containers, requests, errors, and resource usage. Visualizing request latency trends helps identify bottlenecks, while monitoring job metrics enables tracking of task attempts and completions. Automatic alerts can be set up for high error rates, billable instance time, and resource usage to maintain the health and efficiency of services. Datadog also visualizes Cloud Run application performance with Serverless monitoring and distributed tracing, allowing for quick spotting of errors and optimization of service configuration. Finally, Cloud Run logs are automatically collected if using the Datadog Google Cloud integration or instrumented through environment variables or container configurations.