Multi-fluid simulations, especially volume of fluid datasets, confront visualization experts with the challenge of reconstructing appropriate material interfaces that accurately delimit fluid boundaries. In general this reconstruction problem does not have an unique solution, leading to possible spatial and temporal inconsistencies in the reconstructed interfaces. In this paper we present and discuss challenges and directions for topology based analysis of volume of fluid data and its interfaces. We investigate the suitability of established topological methods for solving these challenges, analyze their potential and drawbacks, and propose future research directions.