This paper presents a unified framework for analyzing local and global identification in log linearized DSGE models that encompasses both determinacy and indeterminacy. The analysis is conducted from a frequency domain perspective. First, for local identification, it presents necessary and sufficient conditions for: (1) the identification of the structural parameters along with the sunspot parameters, (2) the identification of the former irrespective of the latter and (3) the identification of the former conditional on the latter. These conditions apply to both singular and nonsingular models and also permit checking whether a subset of frequencies can deliver identification. Second, for global identification, the paper considers a frequency domain expression for the Kullback-Leibler distance between two DSGE models and shows that global identification fails if and only if the minimized distance equals zero. As a by-product, it delivers parameter values that yield observational equivalence under identification failure. This condition requires nonsingularity but can be applied to nonsingular subsystems and across models with different structures. Third, to develop a further understanding of the strength of identification, the paper proposes a measure for the empirical closeness between two DSGE models. The measure gauges the feasibility of distinguishing one model from another using likelihood ratio tests based on a finite number of observations generated by the two models. The theory is illustrated using two small scale and one medium scale DSGE models. The results document that parameters can be identified under indeterminacy but not determinacy, that different monetary policy rules can be (nearly) observationally equivalent, and that identification properties can differ substantially between small and medium scale models.