TITLE: Status of (Global) Langlands Conjecture for $GL_2$ over $\mathbb{Q}$
QUESTION [24 upvotes]: Apologies if this question has already been dealt with on MO. I am wondering about the status of the global Langlands conjectures for $GL_2$ over the rational numbers. How close is humanity to the proof of these conjectures? 
I guess Langlands picture is related to (or, should I say, includes?) the Taniyama-Shimura, Fontaine-Mazur, and Serre Conjectures. There has been great progress on these latter conjectures recently. Even assuming these conjectures are settled, how much closer are we to understanding the Langlands program for $GL_2$? 
It would be helpful if somebody points to a paper where a modern and precise version of the global Langlands conjecture for $GL_2$ is stated. For the local Langlands conjecture, we have the nice paper of Vogan. Is there an analogous paper for the global theory?

REPLY [2 votes]: Additionally to what Joel was saying, Langlands conjectured the existence of a universal group $\widehat{G}$ (depending on the number field only) whose 2-dim'l representation correspond to automorphic representation of GL(2) in a suitable way. These would include automorphic forms with the archimedean factors not being algebraic, e.g., even Maass forms with Laplace eigenvalue $\neq 1/4$. From what I understand, Arthur suggests a definition of $\widehat{G}$ here:  http://www.claymath.org/cw/arthur/pdf/automorphic-langlands-group.pdf. The situation is similar to case (1c) described above.