Due to their relevance in systems analysis and controller design, this thesis considers the problem of determining input-output properties of linear time-invariant systems. While obtaining a suitable mathematical model describing the input-output behavior of a dynamical system can be a difficult task, data of the system in form of input-output trajectories is often and increasingly available. This thesis therefore introduces three complementary data-driven analysis methods to determine input-output properties directly from data without deriving a mathematical model first. In particular, the results of this thesis include iterative methods, where data is actively sampled by performing experiments on the unknown system, as well as approaches based on available (offline) data. All these approaches are simple to apply, come with low requirements on the data, and provide rigorous theoretical guarantees. Systems analysis not only provides insights into the system and allows to do controller design with guaranteed stability, but it can also validate a given controller or its closed-loop performance. By developing different methods to determine input-output properties directly from data on the basis of a rigorous mathematical analysis, this thesis contributes to a sound mathematical framework for data-driven systems analysis and control theory.