Note: this site last updated in 2006
An article from "The Molecules of HIV" (c) Dan Stowell
They have receptors embedded in their membranes, normally little things poking out made of two proteins connected together. T cells' receptors are a bit like immunoglobulins">immunoglobulins, except smaller: where immunolgobulins are shaped like a "Y", the T cell receptor is equivalent to only one of the upper arms of the "Y".
The shape of the T cell receptor is variable. The genes for the immune system encode various different sorts of the subunits that go to make up these receptors: it chooses from these genes at random, making a "pick 'n' mix" protein every single time. As a result there are literally millions of different types of T cell receptor in existence in your body, and each of them is specialised to recognise different "foreign" matter. There are also combinations which lead to receptors which would attack the body's own proteins and cells - but these are checked and destroyed in the thymus (where the T cells mature) before the T cells are let loose in the body.
The T cell receptor might have a variable shape, but there's something constant about all of the shapes: they all need to bind to, not just an antigen, but a complex of an antigen associated with a HLA protein. HLA protein is the signaller present in most cells of the body, which takes bits of stuff and holds it up outside the cell so that it can conveniently be checked by T cells.