The moduli spaces of Higgs bundles and flat connections on a compact Riemann surface of genus > 1 play important roles in several parts of math and mathematical physics, in particular the geometric/analytic Langlands correspondence. For the rank-2 case, I will give an explicit description of these moduli spaces: the method is to use the moduli space of pairs (rank-2 bundle, sub-line bundle) as an auxiliary space. Among the findings are (1) new Lagrangians in the moduli spaces of Higgs bundles, (2) conjectured counter-parts of these Lagrangians in the moduli spaces of flat connections, and (3) explicit description of components of the wobbly locus in the moduli spaces of bundles.