The formation of stars and planets are connected through disks. Our theoretical understanding of disk formation has undergone drastic changes in recent years, and we are on the brink of a revolution in disk observation enabled by ALMA. Large rotationally supported circumstellar disks, although common around more evolved young stellar objects, are rarely detected during the earliest, "Class 0" phase; a few excellent candidates have been discovered recently around both low-and high-mass protostars though. In this early phase, prominent outflows are ubiquitously observed; they are expected to be associated with at least small magnetized disks. Whether the paucity of large Keplerian disks is due to observational challenges or intrinsically different properties of the youngest disks is unclear. In this review we focus on the observations and theory of the formation of early disks and outflows, and their connections with the first phases of planet formation. Disk formation -once thought to be a simple consequence of the conservation of angular momentum during hydrodynamic core collapse -is far more subtle in magnetized gas. In this case, the rotation can be strongly magnetically braked. Indeed, both analytic arguments and numerical simulations have shown that disk formation is suppressed in the strict ideal magnetohydrodynamic (MHD) limit for the observed level of core magnetization. We review what is known about this "magnetic braking catastrophe", possible ways to resolve it, and the current status of early disk observations. Possible resolutions include non-ideal MHD effects (ambipolar diffusion, Ohmic dissipation and Hall effect), magnetic interchange instability in the inner part of protostellar accretion flow, turbulence, misalignment between the magnetic field and rotation axis, and depletion of the slowly rotating envelope by outflow stripping or accretion. Outflows are also intimately linked to disk formation; they are a natural product of magnetic fields and rotation and are important signposts of star formation. We review new developments on early outflow generation since PPV. The properties of early disks and outflows are a key component of planet formation in its early stages and we review these major connections.