What are, really, structural equation models? I can't really find a clear description of how SEMs work, or even whether they are a really unified thing or just a bunch of other methods that people refer to as a whole. The definitions one finds typically say what they can be used for (e.g. find causal relations between variables, while accounting for latent variables), but not really so much about how they do so. How are these models related to any other anonymous hierarchical model with unobserved variables? It seems like for SEMs there are some important components, like observations, with measurement error, and latent variables. But the same components exist in say state space models. Is a state space model a SEM, say? Are there any good readings that explain what SEMs are and how they work? Any good papers with SEMs where the set of equations that makes up the SEM is actually shown? One sees lots of diagrams relating components, but not really the set of equations that are considered or an explanation of what is the technique use to estimate the models parameters? How are models fit to data in SEM? And why is it that these models are apparently much more used in social sciences than in other areas? Are these models known more by other names in different areas?
 A: That's a lot of questions. I'll  try to answer some of them. :)
Bollen's book "Structural Equations with Latent Variables" is one of the best expositions of all of the underlying equations. The basic equations are fairly straightforward - this paper has the equations for confirmatory factor analysis (which is a subset of SEM).
It's a claim that's often made, but saying that you can use SEM to find causal relations between variables makes me pretty uncomfortable. You can use SEM to find causal relations in the same way that you can use regression or correlation analysis to find causal relationships; i.e. you (usually) can't.
SEMs are related to lots of other techniques. Regression (and all GLMs) can be thought of as a case of SEMs. This paper shows how SEM and multilevel models are (or can be) equivalent.
I don't know anything about state-space models, so I can't answer that.
Models are fit to data using maximum likelihood. The papers linked above (hopefully) show that.
I think the models are used more in social sciences for historical reasons. Joreskog developed LISREL (the first SEM program) when he worked at ETS, who do educational testing. They fit social science problems, because social scientists have measures that are not clearly defined, and where the measure is not clear from the definition (e.g. depression, socio-economic status) and so an analysis that looks at relations between variables and at the process for defining these variables at the same time is useful.
