Objective: In the steady-state visual evoked potential (SSVEP)-based brain computer interfaces (BCIs), spatial filtering, which combines the multi-channel electroencephalography (EEG) signals in order to reduce the non-SSVEP-related component and thus enhance the signal-to-noise ratio (SNR), plays an important role in target recognition. Recently, various spatial filtering algorithms have been developed employing different prior knowledge and characteristics of SSVEPs, however how these algorithms interconnect and differ is not yet fully explored, leading to difficulties in further understanding, utilizing and improving them. Methods: We propose a unified framework under which the spatial filtering algorithms can be formulated as generalized eigenvalue problems (GEPs) with four different elements: data, temporal filter, orthogonal projection and spatial filter. Based on the framework, we design new spatial filtering algorithms for improvements through the choice of different elements. Results: The similarities, differences and relationships among nineteen mainstream spatial filtering algorithms are revealed under the proposed framework. Particularly, it is found that they originate from the canonical correlation analysis (CCA), principal component analysis (PCA), and multi-set CCA, respectively. Furthermore, three new spatial filtering algorithms are developed with enhanced performance validated on two public SSVEP datasets with 45 subjects. Conclusion: The proposed framework provides insights into the underlying relationships among different spatial filtering algorithms and helps the design of new spatial filtering algorithms. Significance: This is a systematic study to explore, compare and improve the existing spatial filtering algorithms, which would be significant for further understanding and future development of high performance SSVEP-based BCIs.