European hazelnut (Corylus avellana L.), cultivated in several areas of the world including Europe, Anatolia, and the USA, is an economically important nut crop due to its high mineral, oleic acid, amino acid, and phenolic compound content and pleasant flavor. This study examined molecular genetic diversity and population structure of both Slovenian and Turkish hazelnuts. In the first part of the work, genetic diversity of 54 wild accessions and 48 cultivars from the Slovenian national hazelnut collection was determined using amplified fragment length polymorphism (AFLP) and simple sequence repeat (SSR) markers. The accessions were also characterized for ten nut and seven kernel traits and some wild accessions were shown to have breeding potential. An association mapping panel composed of 64 hazelnut cultivars and wild accessions had considerable variation for the nut and kernel quality traits. Morphological and molecular data were associated to identify markers controlling the traits. In all, 49 SSR markers were significantly associated with nut and kernel traits [P < 0.0001 and LD value (r2) = 0.15–0.50]. This work is the first use of association mapping in hazelnut and has identified molecular markers associated with important quality parameters in this important nut crop. In the second part of the work, 402 Turkish hazelnut accessions were screened with 30 SSR markers. The data obtained from this screen allowed selection of a national core collection of hazelnut. This core collection represents a maximum of genetic diversity in a minimum number of individuals. Turkish cultivar ‘Tombul’ was sequenced using next generation sequencing technology and new SSR markers were developed. It was found that seven SSR markers were sufficient to discriminate Turkish hazelnut cultivars from each other. This study provides molecular information for marker-assisted selection in hazelnut and gives new insight to discover the genetic potential of hazelnut germplasm.