‘must reads’ of ~~contemporary~~ sociology

I missed 'contemporary' in your question and instead wrote about 'the classics' of sociology. I will still post the comment as is, as it might be informative to others, and make another one on contemporary sociology.

Émile Durkheim

... established the research methods of the social sciences. His other main work regards the cohesion of modern society as a consequence of interdependence through the division of labor as opposed to pre-modern societies, which were more 'mechanical' in their solidarity through concepts of kinship, religion and authority.

Max Weber

... lays the foundation of sociology by defining what sociology even investigates, by coining the term social acting, a concious act that is in reaction to the behavior of somebody else.

Karl Marx

... is most famous for his dialectic on class struggle, explaining social change as a phenomenon of class struggle between an upper class and a lower class, with the upper class always eventually being subverted by the limitations and consequences of the nature of their specific power base over the lower class.

Pierre Bourdieu

... expanded the concept of capital into non-economic areas by dividing it into economic, social, cultural and symbolic capital and then used this to explain social stratification and classification through the distributions of those forms of capital over social classes. He is also the father of a lot of other sociological concepts, like field theory.

Bruno Latour

One must read, that is also my favorite theory, is Bruno Latour's actor-network-theory. He extends what is considered an actor to non-human actors and even objects, to which he refers to as actants. He then argues that actors/actants can be viewed as combinations of its parts, which in turn are actors or actants, and further argues that these combinations are capable of more than its parts.

One example he provides is that a speedbump can be viewed as an actant-made police officer. Executing the will (enforcing the speed limit) of the police officer in absentia.

Another one is the human-gun-actor, which is an actor that comes into being through the relation of a human and a gun. Combined capable of more than its individual parts and thus irreducible in its actions to just one of its parts.

Randall Collins

IMO, the leading sociologist on violence. He argues that committing violence is actually very hard and that a confrontational tension has to be overcome to do so. He identified five relational processes through which this can be systematically be achieved, which are combinations of emotional mechanisms.

Anne Nassauer

Since we are on the topic of violence, I would like to point out Anne Nassauer, who, based on Collins' theory developed a set of relational processes to explain police brutality during protests. These processes lead to situational breakdowns, which are defined as the collapse of interactive routines between protesters and police, which heightens the tension between the actors and then releases itself in a moment of emotional superiority.

On topics

I haven't read a journal in some time, so I'm not up to date, but I reckon that old topics always stay relevant.

Social Inequality is always an issue. Topics that frequently came up at uni are on immigration, education and family. I attended interesting seminars on violence (covering domestic violence and genocide), the complex origins of the Arab spring, the health sector and it's declining workforce. I've also seen good quality content on YouTube about the origin and history of systemic alcohol addiction in Russia and how Christianity lead to the nuclear family superseding the tribal family. The other day I realized that Fashion is a sociological microcosm. Sociology is all about looking at human behavior on a greater scale, identifying patterns on these scales and finding explanations for why this or that is the way it is. So you can imagine how broad the variety of topics can be.

Side Note

I guess you could split what sociologists write about into three areas: methodology (how to do science), theories (models of the world) and studies (a specific topic being investigated).