Serre's conjecture for a connected reductive group $G$ over $\Q$ predicts that every irreducible residual Galois representation of G_\Q={\rm Gal}(\bar{\Q}/\Q) taking values in $\widehat{G}(\overline{\F}_p)$ arises from an automorphic representation of $G(\A)$. In the case $G=\GL_2$, the conjecture for odd two-dimensional Galois representations was proved by Khare and Wintenberger. In this talk, I will briefly explain the main ideas of their proof and then introduce my recent work on Galois representations related to $\GSp_4$, with a view toward Serre's conjecture for $\GSp_4$.
