- one domain is computability, which studies what can be computed, and how in a rather abstract sense: largely what is described in Suresh Venkat’s answer.
- another is algorithmics, that finds effective means to compute answers to specific problems, with specific constraints. Computability is a theoretical context for algorithmics.
- semantics (for want of a better name), analyzes the conceptual organization of computational problems, and of algorithms, into higher level concepts, so as to factorize techniques that have proved useful and are often reused, such as the concept of subprogram,data-structures, modules, information hiding. It includes the development of mathematical tools that formalize adequately these concepts to allow high-level reasonning (Scott semantics for example). It also touches on the way this is expressed, thus on the separation and relation between syntax and semantics. Programming languages concepts are part of it (though language design is probably the pratical application of that knowledge). It can also include the relation between proof theory and computation theory, and the modern role of type systems.
- another topic, which could develop more than it has so far, is the relation between computation and fundamental physics. For example. is there a relation between the limits on computation and the properties of the physical world, such as physical information density or the laws of thermodynamics. Quantum computing may improve a bit our computational prowess; could we hope for more? Some may dispute that this is still TCS, though there are TCS studies on hypercomputation.
im a fucking shitlord, nigga
UMA 
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