Subspace-based algorithms that exploit the orthogonality between a sample subspace and a parameter-dependent subspace have proved very useful in many applications in signal processing. The statistical performance of these subspacebased algorithms depends on the deterministic and stochastic statistical model of the noisy linear mixture of the data, the estimate of the projector associated with different estimates of the scatter/covariance of the data, and the algorithm that estimates the parameters from the projector. This chapter presents different complex circular (C-CES) and non-circular (NC-CES) elliptically symmetric models of the data and different associated non-robust and robust covariance estimators among which, the sample covariance matrix (SCM), the maximum likelihood (ML) estimate, robust M-estimates, Tyler's M-estimate and the sample sign covariance matrix (SSCM), whose asymptotic distributions are derived. This allows us to unify the asymptotic distribution of subspace projectors adapted to the different models of the data and to prove several invariance properties that have impacts on the parameters to be estimated. Particular attention is paid to the comparison between the projectors derived from Tyler's M-estimate and SSCM. Finally, asymptotic distributions of estimates of parameters characterized by the principal subspace derived from the distributions of subspace-based parameter estimates are studied. In particular, the efficiency with respect to the stochastic and semiparametric Cramér-Rao bound is considered.