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We explore and compare different ways large-scale structure observables in redshift-space and real space can be connected. These include direct computation in La- grangian space, moment expansions and two formulations of the streaming model. We derive for the first time a Fourier space version of the streaming model, which yields an algebraic relation between the real- and redshift-space power spectra which can be compared to ear- lier, phenomenological models. By considering the redshift-space 2-point function in both configuration and Fourier space, we show how to generalize the Gaussian streaming model to higher orders in a systematic and computationally tractable way. We present a closed- form solution to the Zeldovich power spectrum in redshift space and use this as a framework for exploring convergence properties of different expansion approaches. While we use the Zeldovich approximation to illustrate these results, much of the formalism and many of the relations we derive hold beyond perturbation theory, and could be used with ingredients measured from N-body simulations or in other areas requiring decomposition of Cartesian tensors times plane waves. We finish with a discussion of the redshift-space bispectrum, bias and stochasticity and terms in Lagrangian perturbation theory up to 1-loop order.