Rapid declines in Arctic sea ice have captured attention and pose significant challenges to a variety of stakeholders. There is a rising demand for Arctic sea ice prediction at daily to seasonal time scales, which is partly a sea ice initial condition problem. Thus, a multivariate data assimilation that integrates sea ice observations to generate realistic and skillful model initialization is needed to improve predictive skill of Arctic sea ice. Sea ice data assimilation is a relatively new research area. In this review paper, we focus on two challenges for implementing multivariate data assimilation systems for sea ice forecast. First, to address the challenge of limited spatiotemporal coverage and large uncertainties of observations, we discuss sea ice parameters derived from satellite remote sensing that (1) have been utilized for improved model initialization, including concentration, thickness and drift, and (2) are currently under development with the potential for enhancing the predictability of Arctic sea ice, including melt ponds and sea ice leads. Second, to strive to generate the “best” estimate of sea ice initial conditions by combining model simulations/forecasts and observations, we review capabilities and limitations of different data assimilation techniques that have been developed and used to assimilate observed sea ice parameters in dynamical models.