INTRODUCTION Scientists are asked to describe and understand the complex behavior of natural processes. This is often done in difficult conditions, with instruments detecting specific indicators and providing limited datasets to satisfy knowledge and imagination. Despite these limitations, many studies have been able to provide unprecedented understanding of different processes in nature, albeit often under specific (i.e., simplified) conditions. A progressively more quantitative approach has been often obtained exploiting the latest technological improvements available. The study of volcanic, or more generally, magmatic processes well exemplifies these conditions and progression (Figure 1). Qualitative reports of how volcanoes erupt date back to thousands of years, as the description of the 79 AD Vesuvio eruption from Pliny the Younger; however, most of our qualitative and quantitative understanding of the volcano factory and its various indicators has been definitely achieved in the frame of the technological boost of the last decades. Certainly, the tremendous improvement of the monitoring system of active and erupting volcanoes has allowed detecting many changes in the geophysical, geodetic and geochemical behavior before, during and after eruptions (e.g., Lowenstern et al., 2006; Sigmundsson et al., 2010; Chiodini et al., 2012). As a result, a significant amount of data has been collected on a reasonable amount of active volcanoes worldwide, and it is in general possible to assign some physical or chemical meaning to many detected changes. This knowledge is also crucial to define when a volcano enters a phase of deviation from its baseline, or unrest, which may culminate in an eruption and to forecast any impending eruption. The understanding of the processes occurring within volcanoes, ultimately leading to the geophysical, geodetic and geochemical changes detected at the surface, is supported by analytical, numerical, and experimental models (e.g., Cayol et al., 2000; Gudmundsson, 2006; Caricchi et al., 2007; Ruch et al., 2012). Modeling has reached a relatively sophisticated stage, allowing understanding otherwise inaccessible and/or long-lasting 2D and, to a lesser extent, 3D processes. Similarly crucial to understand the mean to longerterm behavior of volcanoes are many field and petrological-geochemical studies, supported by dating techniques (e.g., Gravley et al., 2007; Thordarson and Larsen, 2007; Collins et al., 2009; Wilson and Charlier, 2009; Corsaro et al., 2013). In particular, field studies prove fundamental in reconstructing the eruptive history of a volcano, including the eruption location, type, size and frequency; petrological and geochemical studies provide an invaluable amount of information on the processes and times characterizing the formation of the magma, its rise and emplacement within the crust, including mixing, mingling, crustal assimilation, and fractionation. These approaches have allowed reaching a dramatic advancement in our understanding of volcanoes. An overview of the major improvements in volcanology in the last decades is beyond the scope of this contribution. For facts, one can refer to the comprehensive, detailed and essential overview of Cashman and Sparks (2013). This includes many of the important studies on the emplacement (formation of magma chambers), rise (eruption triggers, dike propagation), and eruption of magma (conduit construction and evolution, magma rheology and fragmentation, eruptive styles). The described amount of research underlines the impressive efforts made by the volcanological community in considering and analyzing the several complex evolutionary stages of a magma within the volcano factory, from its generation to its eruption. Even though the reached level of knowledge may not unravel the many questions behind the volcano factory, it certainly provides a robust platform to test hypotheses and plan more advanced and sophisticated studies. Indeed, despite the important achievements, modern volcanology still has to fully define and understand several major processes, involving different topics and approaches, and resulting in likewise challenges for the future. Here the first-order processes, or challenges for volcanology, are summarized in an ideal journey from the deepest to the shallowest portions of the volcano factory (Figure 2). Many of these processes may be unraveled not only by observations on volcanoes on Earth, but also on extraterrestrial volcanoes, including those on Venus, Mars and Io. While studies on terrestrial volcanism provide the key to understand also extraterrestrial volcanism, it is likewise expectable that observations on adequately imaged volcanic edifices from Mars and Venus allow to better define volcanic processes on Earth.