Essentially, the scenario in which mergers of smaller units play an important role in the formation of massive elliptical galaxies seems to be consistent with observations. Oser et al. (2010) and Oser et al. (2012) found good agreement with a number of observations, using simulations of the formation of massive galaxies in a two phase process: early dissipation followed by mergers (mostly minor). Formation time-scales should be shorter for more massive systems, a notion that is referred to as the downsizing scenario (Cowie et al. 1996), but not as short as in the monolithic collapse scenario of Eggen et al. (1962).
Classical bulges could also form from mergers (e.g. Aguerri et al. 2001), but the differences outlined above in the properties of classical bulges and ellipticals indicate that different merger histories are needed to form classical bulges, as compared to ellipticals. These differences could be in the ratio of major to minor mergers, the ratio of gas poor to gas rich mergers, the total number of mergers, and the merger orbit parameters (e.g. Hopkins et al. 2010).
The formation of disk galaxies with low bulge/total ratios is still a challenge for CDM cosmology (e.g. Weinzirl et al. 2009), but the past few years saw much progress in this direction (e.g. Governato et al. 2009, Governato et al. 2010, Brook et al. 2011). Scannapieco et al. (2010) reported the formation of bulges via minor mergers, resulting in systems with Sérsic indices around 1 and bulge/total ratios around 0.1-0.2 (consistent with being disk-like bulges - somewhat surprising given the occurrence of minor mergers) but with too large values of re. Using a fully cosmological hydrodynamical simulation, Brook et al. (2012) were able to produce, via a bar, a disk-like bulge with properties similar to observed disk-like bulges, including re, although their bulge/total ratio of 0.21 is at the high tail of the observed distribution in e.g. Gadotti (2009). In this context, it is worth pointing out that at fixed bar/total mass ratio, disk-like bulges are less massive than classical bulges, suggesting that, if disk-like bulges form via bars, further processes are necessary to build classical bulges (Gadotti 2011).
The implementation of the formation of disk-like bulges through bar instabilities in semi-analytical models still needs work, as the disk instability criterion used to set the formation of the bulge is prone to yield wrong results (see Athanassoula 2008, De Lucia et al. 2011, Guo et al. 2011). In addition, the fraction of disk mass converted in a bulge in these simulations tends to be too large, since typically it has to be large enough to marginally re-stabilize the disk, which is at odds with the observation that more than half of disk galaxies have bars (e.g. Menéndez-Delmestre et al. 2007). Relevant to this discussion is the observation that estimates of the mass redistributed by a bar are ≲13 per cent of the mass of the disk (Gadotti 2008).
Finally, there are studies, particularly more recently, on the formation of bulges via the coalescence of giant clumps in primordial disks (see Noguchi 1999, Natureexlaba Immeli et al. 2004, Natureexlabb Immeli et al. 2004, Bournaud et al. 2007, Elmegreen et al. 2008). Bulges formed in this way have properties similar to classical bulges, but unlike bulges built through mergers, they lack a distinctive dark matter component.
Essentially, all research on galaxies aims at answering how galaxies form and evolve, what is the role of the different galactic structural components (such as those outlined in Sect. 2) in this history, and how do they relate with each other. Galaxies are ghostly - we can see through them - which is helpful sometimes, but also means that projection effects can frequently complicate matters. Promising paths are those which link different approaches, such as structural analysis, kinematics and dynamics, stellar population properties and evolution, multi-wavelength work, ample redshift coverage, observations and theory. It is with such holistic thinking that we should pursue the goal of unveiling the physics behind these "majestic", "spectacularly beautiful" stellar systems (using the words of Binney & Tremaine 1987).
Acknowledgements I wish to wholeheartedly thank the organizers, in particular Manuela Zoccali and Giuseppe Bono, for posing such a beautiful challenge to me, and for the hospitality in lovely Erice. It is a pleasure to thank Gabriel Brammer, Oscar Gonzalez, Taehyun Kim and Rubén Sánchez-Jannsen for carefully reading an earlier version of this paper and providing many useful comments. I thank Peter Erwin and Pauline Barmby for helping preparing the Spitzer M31 image for decomposition. This work was co-funded under the Marie Curie Actions of the European Commission (FP7-COFUND).