Moduli spaces of stable parabolic connections on curves are very interesting objects which are related to different area of mathematics like algebraic geometry, integrable systems, mathematical physics and Geometric Langlands conjecture. In this lecture, we will explain about an explicit geometry of the moduli spaces of stable parabolic connections on curves introduced and constructed by Inaba, Iwasaki and Saito and Inaba. Then we will review a work of Arinkin and Lysenko on a rank 2 connections on the projective line with 4 singular points, which is related to Geometric Langlands conjecture in this case. We then explain about the joint work on the moduli space of rank 2 parabolic bundles on the projective line with Simpson and Loray. If time permits, related works of Geometric Langlands conjecture in these cases may be discussed.