In this talk, we explore the development and analysis of multigrid solvers for biharmonic equations discretized using isogeometric analysis (IGA). Our focus lies on handling C1-smooth multi-patch domains, which can be used for fourth-order partial differential equations (PDEs). Such problems arise in simulations of structural properties of thin plates and shell structures, discretized with multi-patch spline parameterizations. Following the works [Collin et al., CAGD, 2016] and [Kapl et al., CAGD, 2017], we consider analysis-suitable G1 multi-patch parametrizations that ensure C1-smooth discretizations. Building on the robust multigrid framework introduced in [Sogn and Takacs, CMA, 2019], we investigate efficient two-level refinement relations and analyze the block structures of smoothing matrices to improve computational performance. Moreover, we aim to extend the methodology to C1-smooth constructions over arbitrary multi-patch surfaces as discussed in [Farahat et al., CMAME, 2023]. Through numerical experiments on a two-patch domain, we aim to compare the performance of different multigrid solver setups. Additionally, we examine how the underlying spline parameterization influences convergence of the solver. This research is part of the ongoing project "Isogeometric multi-patch shells and multigrid solvers".