This paper reviews and evaluates three approaches to controlling the familywise error rate (FWE) in functional neuroimaging: Bonferroni, random field, and permutation tests. Functional neuroimaging data involves a massive multiple testing problem with up to 100,000 correlated test statistics. FWE is the standard measure of Type I errors in multiple testing, and the paper evaluates these methods using simulations and real datasets. Bonferroni methods, including Hochberg's, are applicable to dependent data and are used to control FWE by adjusting thresholds. However, they offer little improvement over traditional Bonferroni. Random field methods use the smoothness of the image to adapt to the severity of the multiple testing problem. Permutation and bootstrap methods, which are computationally feasible with modern computing power, are also evaluated. The permutation method offers substantial improvement over the random field method for low smoothness and low degrees of freedom. The paper highlights the limitations of assuming an equivalent number of independent tests for correlated data. It also discusses the importance of strong FWE control, which allows for the localization of significant voxels, essential in neuroimaging. The maximum statistic plays a key role in FWE control, and its distribution under the null hypothesis is used to determine thresholds. The paper reviews step-up and step-down tests, and the concept of an equivalent number of independent tests. It also discusses the strengths and weaknesses of random field theory (RFT), which accounts for spatial dependence and smoothness. RFT methods are flexible and widely used in neuroimaging, but they rely on assumptions about the data's distribution and smoothness. Resampling methods, including permutation and bootstrap, are evaluated as alternatives to RFT. These methods do not rely on assumptions about the data's distribution and can provide accurate FWE control. However, they are computationally intensive and may not be widely used due to their complexity. The paper concludes that while RFT methods are powerful for smooth data, they may not perform well for low smoothness. Permutation methods offer better performance in such cases. The paper also discusses the importance of using voxel-level statistics with a common null distribution for accurate FWE control. Overall, the paper provides a comprehensive review and evaluation of FWE control methods in functional neuroimaging.This paper reviews and evaluates three approaches to controlling the familywise error rate (FWE) in functional neuroimaging: Bonferroni, random field, and permutation tests. Functional neuroimaging data involves a massive multiple testing problem with up to 100,000 correlated test statistics. FWE is the standard measure of Type I errors in multiple testing, and the paper evaluates these methods using simulations and real datasets. Bonferroni methods, including Hochberg's, are applicable to dependent data and are used to control FWE by adjusting thresholds. However, they offer little improvement over traditional Bonferroni. Random field methods use the smoothness of the image to adapt to the severity of the multiple testing problem. Permutation and bootstrap methods, which are computationally feasible with modern computing power, are also evaluated. The permutation method offers substantial improvement over the random field method for low smoothness and low degrees of freedom. The paper highlights the limitations of assuming an equivalent number of independent tests for correlated data. It also discusses the importance of strong FWE control, which allows for the localization of significant voxels, essential in neuroimaging. The maximum statistic plays a key role in FWE control, and its distribution under the null hypothesis is used to determine thresholds. The paper reviews step-up and step-down tests, and the concept of an equivalent number of independent tests. It also discusses the strengths and weaknesses of random field theory (RFT), which accounts for spatial dependence and smoothness. RFT methods are flexible and widely used in neuroimaging, but they rely on assumptions about the data's distribution and smoothness. Resampling methods, including permutation and bootstrap, are evaluated as alternatives to RFT. These methods do not rely on assumptions about the data's distribution and can provide accurate FWE control. However, they are computationally intensive and may not be widely used due to their complexity. The paper concludes that while RFT methods are powerful for smooth data, they may not perform well for low smoothness. Permutation methods offer better performance in such cases. The paper also discusses the importance of using voxel-level statistics with a common null distribution for accurate FWE control. Overall, the paper provides a comprehensive review and evaluation of FWE control methods in functional neuroimaging.