In the hybrid model, the processing of your jobs/assets happens in your compute infrastructure.
In the processing, there is some information that is sent to Dagster Cloud to help keep track the state of these computations. For example, the event logs are stored within Dagster Cloud (e.g. when the run has started, which steps have run, what resources were initialized).
Also, any loggers that you want to be managed by Dagster Cloud currently store their logs in our backend so that they’re searchable through the UI. But we’re working to make this customizable so that these logs can be sent to some storage that you own (e.g. your own S3 bucket).