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In recent times, two terms, which are being usedmore andmore frequently have been introduced into scientific nomenclature: Geoheritage (cf. Reynard and Brilha 2018 and references therein) and Geodiversity (cf. Gray 2013, 2018 and Najwer and Zwoliński 2014 and references therein). The concept of geoheritage was introduced in the 1970s (cf. Martini 1994), whereas geodiversity has been recognised as a concept worth investigating from the 1990s onwards (e.g. Wiedenbein 1993; Sharples 1995) but several recent attempts have been made to properly define and assess it (cf. Zwoliński et al. 2018 and references therein). Since their appearance, both concepts have aroused strong interest and debate, not only of researchers in Earth Sciences but also of experts in biology (e.g. Parks and Mulligan 2010; Hjort et al. 2012), spatial planning (e.g. Poiraud et al. 2016; Gordon et al. 2018; Bruschi and Coratza 2018 and references therein), general tourism (cf. Newsome and Dowling 2018 and reference therein) as well as national geotourism (e.g. Asrat et al. 2008 for Ethiopia and Migoń 2012 for Poland and references therein) and cultural heritage (e.g. Margottini 2007; Přikryl and Torok 2010; Coratza et al. 2016; Reynard et al. 2017), especially those interested in integrated and interdisciplinary approaches. This increase in awareness is testified within scientific circles by the numerous scientific conferences, workshops and sessions on geoheritage and geodiversity issues organised during the last two decades. Worthy of note is the increasing success from 2013 of the joint session on geoheritage and geodiversity in the European Geosciences Union General Assembly, which demonstrates the importance of heritage issues to the geoscience community. This issue ofGeoheritage comprises nine papers presented at the session BGeoheritage and Geodiversity Matter: Themes, Links and Interactions^ held in Vienna in April 2016 at the European Geosciences Union General Assembly. The papers focus on current methods of research and debates on geodiversity and geoheritage in international as well as national scientific circles, from the global to the local scale. The four first texts deal with methodological issues. Clivaz and Reynard discuss the issue of inventorying the so-called invisible geomorphosites, i.e. former landforms destroyed or hidden by human activities, a key issue in highly humanised regions (such as urban areas; cf. Reynard et al. 2017) where the original geomorphology has been highly modified by anthropogenic activities. The inventorying issue is also discussed in the paper written by Mauerhofer et al., which propose an inclusive and systematic approach of protection and outreach of the geomorphological heritage based on a geomorphosite inventory in the Simien Mountains National Park in Ethiopia. The article not only describes the various steps of the inventory and the used assessment method; it also discusses the problems related to geoheritage protection in developing countries and proposes a road map for the geomorphosites management. Araujo and Pereira propose an upgrade of a method for the geodiversity quantitative assessment elaborated by Pereira et al. (2013). In particular, the authors propose to consider water-related elements as a geodiversity component, including the Water Resources Index in the set of indicators for the geodiversity evaluation. Betard and colleagues describe geodiversity and threats in the Araripe basin (Brasil), considered as a major geodiversity hotspot at a global scale, and propose a general approach for the assessment of geodiversity. The following papers are related to the interactions between geoheritage, geodiversity and cultural diversity and * Paola Coratza [email protected]