When comparing relations and means of latent variables, it is important to establish measurement invariance (MI). Most methods to assess MI are based on confirmatory factor analysis (CFA). Recently, new methods have been developed based on exploratory factor analysis (EFA); most notably, as extensions of multi-group EFA, researchers introduced mixture multi-group EFA, multi-group exploratory factor alignment, EFA trees, and multi-group factor rotation to resolve rotational indeterminacy in EFA. The main advantage of EFA-based (compared to CFA-based) assessment of MI is that no potentially too restrictive measurement model has to be specified. This allows for a more thorough investigation because violations of MI due to cross-loadings can be considered, too. For each method, we address the model specification and recommendations for application, detailing their strengths and weaknesses. We demonstrate each method in combination with multi-group factor rotation in an empirical example. Differences to and possible combinations with CFA-based methods are discussed.