AWS Lambda has evolved from its initial form of executing code from zip files to supporting containerized applications, providing a flexible and scalable compute service that auto-manages resources in response to events. This development has made it appealing for developers who are accustomed to using containers, as it simplifies deploying applications without the overhead of managing Kubernetes clusters. By leveraging AWS Lambda's aggressive scaling capabilities, including automatic scaling to zero when idle, users can efficiently run applications such as a simple web proxy with minimal cost and complexity. The process of deploying a containerized application involves creating a TypeScript Lambda, testing it locally with Docker, pushing the image to Amazon's Elastic Container Registry (ECR), and setting up the Lambda function with the container image. Continuous deployment can be achieved by utilizing tools like Earthly for building and deploying updated container images, ensuring that applications are kept current with minimal manual intervention.