Understanding of olfactory dysfunction in Alzheimer's disease (AD) remains limited. In particular, it is not known how early in the course of the disease olfactory deficits occur, and whether they are restricted to identification or involve other aspects of olfaction. We studied olfactory (odor detection thresholds, quality discrimination, and identification) and cognitive (attention, reasoning, memory, naming and fluency) functioning in patients with AD, with mild cognitive impairment (MCI), and in normal elderly control (NEC) participants. MCI patients were impaired in olfactory sensitivity and identification, while a discrimination deficit was accounted for by abnormal thresholds. AD patients were impaired in all three domains, and were worse than the MCI group. Odor discrimination (OD) and identification performance correlated more prominently than detection thresholds with performance on neuropsychological tests. We concluded that deficits in olfactory detection thresholds and identification occur early in AD, before clinical symptoms are fully developed, and decline further over the course of the disease. High detection thresholds, together with impaired identification, may be useful as an early indicator of AD.