Google Cloud Run is a distinctive serverless compute service that stands out due to its use of Docker as a deployment package, allowing developers to utilize any language, runtime, framework, or library capable of responding to HTTP requests. It features automatic scaling, including the ability to scale to zero, which ensures cost-efficiency by charging only for consumption without fixed costs or management overhead. Cloud Run is optimized for stateless web applications, employing ephemeral containers with execution limited to 15 minutes. The service is compared to alternatives like Google Cloud Functions, AWS Fargate, and Azure Container Instances, highlighting its unique capabilities such as handling HTTP requests, absence of cluster management, and elastic scalability. Additionally, Cloud Run's pricing model is entirely consumption-based, offering potential cost advantages for concurrent request handling when compared to similar services. The text also includes a tutorial on deploying Cloud Run services using Pulumi, including steps for enabling the service, deploying a pre-built container image, and setting up a custom Ruby application.