  Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper
of V. Arnold. In this paper we present a collection of open problems along with
several new constructions in fluid dynamics and a concise survey of recent
developments and achievements in this area. The topics discussed include
variational settings for different types of fluids, models for invariant
metrics, the Cauchy and boundary value problems, partial analyticity of
solutions to the Euler equations, their steady and singular vorticity
solutions, differential and Hamiltonian geometry of diffeomorphism groups,
long-time behaviour of fluids, as well as mechanical models of direct and
inverse cascades.
