A search of published literature reveals 54 western reports of candidate naked-eye sunspot observations made before sunspots were first viewed by telescope in 1610. Most have not had critical scrutiny. Criteria for assessing the reports are presented and each report is reviewed accordingly. Brief extracts from original texts are provided, with translations and full documentation of sources. The review identifies 20 cases that are either misdated or attributable to other phenomena, 15 cases that lack evidence, and six cases that are no more than plausible sunspots. A total of 13 reports are assessed as probable sunspot observations, of which 11 can be dated to within a year. Of these, auroral records suggest that up to six may be associated with possible geomagnetic storms. An apparent match in the timing of seven western observations with sunspot records from East Asia is identified and its implications are discussed.