Magnetic reconnection allows adjacent magnetized plasmas to interact and convert magnetic energy into kinetic energy, energizing the constituent particles of the plasmas. The Magnetospheric Multiscale (MMS) mission, launched by NASA, was designed to study reconnection. The four identical MMS spacecraft in Earth orbit take high-resolution measurements while passing through regions of space plasma where reconnection is occurring. The small-scale, electron-driven physics inside of the central electron diffusion region (EDR) of a reconnection site were not accessible to previous missions before MMS due to limitations of temporal instrument resolution. We present a collection of 32 encounters during which the spacecraft passed through or very near an asymmetric EDR at Earth’s dayside magnetopause. Despite many events occurring near the subsolar magnetopause region, significant differences in upstream plasma conditions still exist, and produce considerable contrasts in the electron velocity space and associated plasma waves. Several distinct types of waves are observed near the EDR, but the biggest fluctuations are seen inside of the thin electron current layer nearest the X-line, which displaces the layer by distances on the order of the layer’s thickness, and produces very localized electric field oscillations of large amplitude (~100 mV/m). Electron-scale turbulence is greatest on the low-density side of asymmetric reconnection, near the electron flow stagnation region along the magnetospheric (low mass density side) separatrix. Generally, we find good agreement with 2D and 2.5D computational models of asymmetric reconnection, although 3D simulations may be required to reproduce the small-scale turbulence seen by MMS. We focus on several EDR events where an in-plane magnetic null (or X-line) reforms in a location separate from a previous null. Flux ropes of varying scale-sizes result. Significant variations in the rate at which magnetic field lines are reconnected on electron timescales can be remotely inferred when MMS is on newly-opened field lines downstream of the X-line, and/or near the EDR. Electron-scale reconnection rate variations, including X-line dissolution and reformation, roughly average out over longer timescales to support a steadier ion-scale reconnection rate. A better understanding of electron-scale reconnection will help with progress towards stable magnetic confinement fusion.