This tutorial review details the rationale and implementation of topographic ERP analyses that use reference-free spatial information from high-density electrode montages to extract statistical information about response strength, latency, and topography across experimental conditions. These methods provide additional neurophysiological interpretability beyond traditional waveform analyses. The example of somatosensory evoked potentials (SEPs) in response to hand stimulation is used to illustrate these points. The tutorial provides conceptual and mathematical descriptions of each analysis step, explaining what is yielded and how to interpret the statistical outcomes. Topographic analysis methods are intuitive and reduce guesswork in ERP research, helping identify information in high-density ERP datasets. The review highlights the limitations of traditional ERP waveform analyses, which are reference-dependent and can lead to biased interpretations. Topographic analyses, however, are reference-independent and provide more complete and interpretable results. The review discusses global field power (GFP) and global dissimilarity (DISS) as reference-independent measures of response strength and topography, respectively. GFP is a single measure of response strength, while DISS quantifies differences in topography between conditions. These measures allow for statistical analysis of topographic modulations without prior selection of time periods or electrodes. The review also addresses the use of average reference in EEG/ERP analyses, emphasizing its role in inverse solution methods and the importance of adequate sampling of the electric field at the scalp. The use of topographic pattern analysis and single-subject "fitting" is discussed, along with clustering algorithms such as k-means and hierarchical clustering (AAHC) for identifying periods of topographic stability. The optimal number of template maps is determined using criteria such as cross-validation and the Krzanowski-Lai criterion. These methods enable the analysis of ERP data in a reference-independent manner, providing more accurate and interpretable results for neurophysiological questions.This tutorial review details the rationale and implementation of topographic ERP analyses that use reference-free spatial information from high-density electrode montages to extract statistical information about response strength, latency, and topography across experimental conditions. These methods provide additional neurophysiological interpretability beyond traditional waveform analyses. The example of somatosensory evoked potentials (SEPs) in response to hand stimulation is used to illustrate these points. The tutorial provides conceptual and mathematical descriptions of each analysis step, explaining what is yielded and how to interpret the statistical outcomes. Topographic analysis methods are intuitive and reduce guesswork in ERP research, helping identify information in high-density ERP datasets. The review highlights the limitations of traditional ERP waveform analyses, which are reference-dependent and can lead to biased interpretations. Topographic analyses, however, are reference-independent and provide more complete and interpretable results. The review discusses global field power (GFP) and global dissimilarity (DISS) as reference-independent measures of response strength and topography, respectively. GFP is a single measure of response strength, while DISS quantifies differences in topography between conditions. These measures allow for statistical analysis of topographic modulations without prior selection of time periods or electrodes. The review also addresses the use of average reference in EEG/ERP analyses, emphasizing its role in inverse solution methods and the importance of adequate sampling of the electric field at the scalp. The use of topographic pattern analysis and single-subject "fitting" is discussed, along with clustering algorithms such as k-means and hierarchical clustering (AAHC) for identifying periods of topographic stability. The optimal number of template maps is determined using criteria such as cross-validation and the Krzanowski-Lai criterion. These methods enable the analysis of ERP data in a reference-independent manner, providing more accurate and interpretable results for neurophysiological questions.