Space infrastructures have become an underpinning of modern society, but their associated cyber risks are little understood. This Dissertation advances the state-of-the-art via four contributions. (i) It introduces an innovative framework for characterizing real-world cyber attacks against space infrastructures, or space cyber attacks, including a novel methodology for coping with missing data and three novel metrics. A case study demonstrates the usefulness of the framework on 108 real-world space cyber attacks. (ii) This Dissertation characterizes the state-of-the-practice in space cyber risk analysis and mitigation, namely the Notional Risk Scores (NRS) within the Space Attack Research and Tactic Analysis (SPARTA) framework. (iii) We propose a set of desired properties that should be satisfied by any competent space cyber risk analysis and mitigation tool and applies them to assess two industrial space cyber risk analysis and mitigation tools. (iv) The study introduces a novel framework to analyze and mitigate space cyber risks by explicitly modeling space cyber attack cascading effects and presenting algorithms for mission risk analysis and mission hardening. We demonstrate the usefulness of the framework by applying it to analyze and mitigate space cyber risks, with testbed-based validation.