The amyloid hypothesis asserts that excess production or reduced clearance of the amyloid-β (Aβ) peptides in the brain initiates a sequence of events that ultimately lead to Alzheimer's disease and dementia. The Aβ hypothesis has identified BACE1 as a therapeutic target to treat Alzheimer's and led to medicinal chemistry efforts to design its inhibitors both in the pharmaceutical industry and in academia. This review summarizes two distinct categories of inhibitors designed based on conformational states of "closed" and "open" forms of the enzyme. In each category the inhibitors are classified based on the core catalytic interaction group or the aspartyl binding motif (ABM). This review covers the description of inhibitors in each ABM class with X-ray crystal structures of key compounds, their binding modes, related structure-activity data highlighting potency advances, and additional properties such as selectivity profile, P-gp efflux, pharmacokinetic, and pharmacodynamic data.