The MlflowClient object provides two primary methods for querying past runs programmatically in MLflow:

1. client.search_runs(experiment_id): This is the recommended method for querying past runs. It allows for flexible searches based on various criteria, including experiment ID, run status, and custom parameters. You can specify search filters as key-value pairs to narrow down the results.

2. client.list_runs(experiment_id): This method offers a simpler approach to retrieve all past runs associated with a specific experiment by its experiment ID, without the need for specifying search filters.

Other options like client.query_runs(experiment_id), client.find_runs(experiment_id), and client.get_past_runs(experiment_id) are not the most suitable choices as client.search_runs is the more commonly used and documented function for programmatic querying in the MlflowClient API.

In summary, for programmatic querying of past runs in MLflow, use client.search_runs(experiment_id) for targeted searches and client.list_runs(experiment_id) for retrieving all runs within an experiment.