A G_2-manifold is a compact Riemannian manifold whose holonomy is the exceptional Lie group G_2. The deformation theory of compact G_2-manifolds is well understood, but the metrics with holonomy G_2 cannot be written down explicitly. In the non-compact case, there exist many examples of such metrics, but there is not much known about their moduli spaces. If we assume that the metric has a fixed asymptotic behavior the problem becomes more approachable. We discuss the results of Karigiannis and Lotay on the deformations of G_2 conifolds and an ongoing research project with Johannes Nordström on asymptotically locally conical G_2-manifolds.