Docker is a lightweight container engine that leverages a versioned copy-on-write file system and declarative builds, allowing users to create Docker images from Dockerfiles, which can then be instantiated into containers. Unlike Vagrant, Docker uses a lightweight isolated process on the host OS, eliminating the need for a full-blown OS for each instance and supporting efficient layer-based image management. Docker Compose utilizes a YAML file to define and manage multiple Docker images collaboratively, making it ideal for testing web apps and databases in concert. Kubernetes manages clusters of Docker containers and supports features like health-monitored rollouts for near-zero downtime deployments. At TestRigor, Docker is employed for establishing declarative deployment images, Docker Compose for local testing and integration, and Kubernetes for projects requiring continuous deployment capabilities.