I think these will go better here as they aren't really mutually incompatible ideologies but someone can move this to the other sticky if you feel the need.
Structural MarxismA school of thought which combines Marxism with Structuralism, it arose in France during the 1960's under the tutelage of Louis Althusser. Structural Marxism constituted simultaneously a revolt against the abandonment of historical thinking in Structuralist philosophy and the perceived historicism of Hegelian Marxism, whilst reaffirming the determinate role of economic factors. Althusser sought to remove what he saw as ideological impurities from Marx and reconstitute it as a fully scientific programme, in opposition to both Historicism and Positivism.
Structural Marxism posits that under a capitalist mode of production the State, law, political discourse, education, religion and other social phenomenon take on specifically capitalist forms in which the logic of capitalist system is reproduced and reflected in the social superstructure.
Further Reading:
For Marx (L Althusser)
Reading Capital (L Althusser)
Althusser and the Renewal of Marxist Social Theory (R Resch)
Political Power and Social Classes (N Poulantzas)
Hegelian MarxismBroadly speaking any form of Marxism which emphasises the role of Hegelian elements or is seen to interpret Marx through Hegel. Although the term is rarely used by thinkers to identify themselves, the trend is usually traced back to Lukács and Korsch and has been closely intertwined with the broad 'Western Marxist' camp.
Some go further and trace the Hegelian interpretation of Marx to Engels himself, arguing that the dialectical philosophy developed by Engels in his later life bore as much in common with Hegel as it did with Marx.
Further Reading:
History and Class Consciousness (G Lukács)
The Young Hegel (G Lukács)
Marxism and Philosophy (K Korsch)
Marx's Grundrisse and Hegel's Logic (H Uchida)
Marxist HumanismA Marxist variant of Humanism, Marxist Humanists typically lay emphasis on Marx's theory of alienation and related elements of Marxist theory, particularly drawing from Marx's earlier works. Various Marxist Humanist trends emerged largely independently from the Praxis School in the East to Trotskyist variants in the West.
Marxist Humanism tends to grant a role for subjective human agency within Historical Materialism, and Marxist Humanists have often been particularly concerned with studying the field of ethics from a Marxist perspective.
Further Reading:
Marx's Humanism Today (R Dunayevskaya)
Analytic Marxism (or, Positivist Marxism)
Analytic Marxism was an attempt to reconstruct Marxism within the framework of Analytic philosophy. It was briefly popular in the Anglo-sphere during the 1980's. Analytic Marxists rejected dialectical logic, the labour theory of value seeking to re-derive Marxist theory using formal logic and neoclassical economics.
Using concepts in neoclassical economics Analytic Marxists developed their own theory of exploitation which claimed that labour played no special role but that exploitation could be shown to arise as a natural consequence of market exchange. Their theory of exploitation stood in contrast to that of classical Marxism in which exploitation was seen to occur primarily at the point of production, not exchange.
Analytic Marxists were divided on the question of whether a theory of history and the development of productive relations could be reconstructed within the Analytic framework. Those who did not reject such a theory outright developed it as a technologically determinist theory. Devoid of class based theory of history they attempted to redefine Marxism as a formulation of applied social and economic justice, rather than a scientific theory.
Further Reading:
Karl Marx's Theory of History (G Cohen)
General Theory of Exploitation and Class (J Roemer)
Making Sense of Marx (J Elster)
A Theory of Justice (J Rawls)
Also, someone may wish to flesh out the Marxist Humanism part, my backgrounds not too strong in that area.