Malaria has been one of the strongest selective pressures on our species. Many of the best-characterized cases of adaptive evolution in humans are in genes tied to malaria resistance. However, the complex evolutionary patterns at these genes are poorly captured by standard scans for non-neutral evolution. Here we present three new statistical tests for selection based on population genetic patterns that are observed more than once among key malaria resistance loci. We assess these tests using forward-time evolutionary simulations and apply them to global whole-genome sequencing data from humans, and thus we show that they are effective at distinguishing selection from neutrality. Each test captures a distinct evolutionary pattern, here called Divergent Haplotypes, Repeated Shifts, and Arrested Sweeps, associated with a particular period of human prehistory. We clarify the selective signatures at known malaria-relevant genes and identify additional genes showing similar adaptive evolutionary patterns. Among our top outliers, we see a particular enrichment for genes involved in erythropoiesis and for genes previously associated with malaria resistance, consistent with a major role for malaria in shaping these patterns of genetic diversity. Polymorphisms at these genes are likely to impact resistance to malaria infection and contribute to ongoing host-parasite coevolutionary dynamics.