On Gramsci's Theory of Society:
Gramsci is best known as a theorist of hegemony, of how capitalist rule has been so resilient despite recurring crises, particularly those that led to the ascent of fascism in his home Italy, but also of how revolution achieved apparent success in 'the East' (he means Russia). This is his starting point. Economically, Gramsci is pretty orthodox in his Marxism. Like Marx, Gramsci argues that from "contradictions"* inherent in the the economic base of society arise crises fraught with conflict, and in turn social change or suppression thereof during such periods. However, it is only in terms of an ideological superstructure that individuals realize mere partial, distorted consciousness of these social forces that drive them. However, for Gramsci, the concrete details of industrial capitalism's maturation accord ideology a new role and produce the participants who take on such ideological roles.
Namely, continuingly increasing specialization in the forces of production (ie, the 'technical division of labor') has impelled the development of organic intellectuals. First, technical specialists emerged, tasked with understanding, organizing, and sometimes leading firms (or groups on a similar level of analysis). With further specialization and elaboration of political apparatuses, further specialists emerged, charged with the task of understanding the social class to which they 'attach' functionally and facilitating this class's organization, mobilization, and fulfillment of its interests. So while the finance capitalist could be said to be a 'proto-organic intellectual' of the capitalist class, it is the lobbyist or elected official who comes to function as an organic intellectual proper, helping to organize the capitalist class as a whole, to realize its shared, long-term interests politically. Similarly, we see according development of the organic intellectual of the working class, moving from trade unionism to party politics to revolutionarily oppositional seizure of capital by workers (at least this was the case with Gramsci's flirtations with Italian syndicalism) (this should sound similar to Marx and Lenin, but Gramsci actually provides a plausible mechanism). I should also note that classes in decline produce organic intellectuals too. Gramsci argues that intellectuals specializing in practices like literary study are actually organic intellectuals bound to the 'petite bourgeoisie' (in this case, the remnants of the prior declining nobility and to some extent independent artisan-producers).
For Gramsci, capitalism has remained so resilient even in crisis because of the success afforded by the organic intellectuals of the capitalist class in maintaining hegemony, through both material and ideological means. First and foremost, the dominant class will offer material concessions to those they dominate and exploit in exchange for complicity with status-quo social relations. Typically, the state functions as the primary tool to administer such. This process is active and apparent to those involved, subject to constant struggle and negotiation. The most paradigmatic and readily familiar example is the response of the state to the threat of socialist revolution in the US during the early 1930s, establishing the welfare-state proper. These concessions facilitated continuing, stable accumulation by the capitalist class as a whole; the state functioned to guarantee hegemony in a way groups of competing capitalists could not.
Hegemony is also exercised ideologically, in two ways: first, the political organizations of the dominant class must fashion a forward-looking plan, presented as catering to the general interests of society (this later characteristic appearing pretty clearly in Marx's original writings). Second, well-entrenched capitalist social practices are naturalized over time, the ideological refraction of these practices concealing their root in class-oppression. Most crucially (and enduringly, spanning hundreds of years), we find ourselves inclined to view capitalist economic activity in terms of exchange of commodities and currency among 'formal' (that is, juridical) equals, the conditions of domination and exploitation that shape such exchanges concealed within economic firms' internal practices, made possible mainly by historical legacy of ownership (also found in Marx); put simply, we obey the edicts of our employers because we recognize the validity of their purchase of our labor and claims to ownership of capital. To reject this framework is to oppose what we usually consider natural, unencumbered individual behavior.**
So what of resistance? For Gramsci, the organic intellectuals of the subordinated class must fashion counterhegemonic ideology and organization, presenting an alternative vision for future society and a planned route theretoward, also cast as being in the collective societal interest. They unfortunately usually can't provide many material 'concessions', particularly prior to and in the early stages of revolution, as subordination of economic class entails exploitation. So in further describing counterhegemony, Gramsci elaborates via the (apparent?) dichotomy between the "war of position" and "war of movement". The war of position is struggle for ideological counterhegemony (or maintenance of hegemony, in the case of the dominant class) and establishment or protection of according facilitating organizations, involving transformation or maintenance of all institutions with ideological functions.
On the other hand, the war of movement involves overt, forcible seizure and/or destruction of physical structures and person-to-person violence (or forcible prevention thereof). Gramsci argues that in advanced capitalist societies, hegemony is so ideologically resilient that forcible destruction of capitalist political institutions (ie, a war of movement) is insufficient to establish counterhegemony. Eg, imagine that the entire Washington Mall, the President, his or her top officials, and all federal legislators were destroyed immediately. Gramsci would argue that civil societal institutions and according guiding ideologies would lead us to rebuild a functionally similar capitalist polity (this runs quite roughly parallel to Weber's argument that coups seizing but leaving intact bureaucratized states have nearly entirely replaced revolutions-proper in the modern and contemporary periods), hence the lack of revolution in the industrial capitalist West of his time. However, in contexts where civil society has failed to develop sufficiently, revolutionaries may wage a war of movement with little attention to war of position, shaping civil society in their image once having seized those apparatuses of domination, hence the apparent success of Soviet revolution (but what became of Soviet civil society? What does this say about Gramsci's schematic?). But borrowing from Gramsci temporarily, I don't think that it's that useful to treat the above schematic strictly dichotomously, nor should we necessarily think of these struggles as temporally successive steps.
Bringing things forward:
How does Gramsci speak to contemporary social dynamics, both those of stability and reproduction and those of transformation? How do prior revolutionary struggles speak to Gramsci? How and where should we attempt to steer contemporary social change (or maintain its stability, for those of you who are more right-wing

)?
ebola
*We must understand "contradiction" as a Marxist-Hegelian dynamic: the present structure of affairs presents the possibility of further realization of human actualization through cooperative laboring, but these possibilities remain unrealized due to how domination by social class suppresses novel, creative collaboration. To resolve such contradiction, communist revolution must excise the class-order (and abolish social classes in general), allowing for unfettered, participatory creative transformation of the external (and social) world. Why "Hegelian"? This schematic mirrors Hegel's account of how consciousness realizes its potential for autonomy, initially through opposition of subject and object via differentiation and experience thereof, but later through transcendence of this conceptual opposition through practices of self-consciousness (involving successively elaborated meta-cognition).
**Why do we think like this? Part of the story is reification: while we view social practices, relations, and actors in terms of seemingly stable representations that emerge within such practices as coordinating cognitive tools, we lose sight of how these practices undergo fluid, uneven transformation throughout history, and even come to mistake static representations for that which they (distortedly) signify. This is merely the beginning of the story of ideology though...