Statistics helps scientists decide what their data show, but its most familiar tool, the $p$-value, is widely misunderstood. Between 2016 and 2026, professional bodies issued new guidance, and researchers developed or popularised alternatives and complements: compatibility intervals, equivalence tests, Bayes factors, and e-values that remain valid when data are checked repeatedly. Reporting rules for trials and reviews were also rewritten. Yet practice has changed little: in the biomedical literature, about 96\% of papers that report $p$-values still include at least one below 0.05. This review argues that much of the confusion comes from treating these numbers as interchangeable. Each inferential procedure carries an intended interpretation and, where applicable, a formal guarantee, such as a 5\% false-alarm rate, that holds only if the study was run and analysed in a particular way. We call this the Claim--Design--Guarantee framework: a result licenses a claim only when the claim, the design (assignment, sampling, monitoring, selection, and analysis), and the guarantee of the method are aligned. We trace the main developments of the decade, explain each tool in plain terms with formal details in boxes, and show with reproducible examples when the choice of tool changes the conclusion. For example, in a simulated two-group study with 100 interim looks, repeatedly applying an unadjusted $p<0.05$ rule produced false positives in 37.6\% of studies, whereas the particular anytime-valid e-value procedure we used produced 2.2\%, below its theoretical 5\% upper bound. We end with a decision tree, a method-selection table, and a step-by-step workflow linked to current reporting guidelines.

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