The anomalous level of electron thermal transport inferred in magnetically confined configurations is one of the most challenging problems for the ultimate realization of fusion power using toroidal devices: tokamaks, spherical tori and stellarators. It is generally believed that plasma instabilities driven by the abundant free energy in fusion plasmas are responsible for the electron thermal transport. The National Spherical Torus eXperiment (NSTX) (Ono et al 2000 Nucl. Fusion40557) provides a unique laboratory for studying plasma instabilities and their relation to electron thermal transport due to its low toroidal field, high plasma beta, low aspect ratio and large flow shear. Recent findings on NSTX have shown that multiple instabilities are required to explain observed electron thermal transport, given the wide range of equilibrium parameters due to different operational scenarios and radial regions in fusion plasmas. Here we review the recent progresses in understanding anomalous electron thermal transport in NSTX and focus on mechanisms that could drive electron thermal transport in the core region. The synergy between experiment and theoretical/numerical modeling is essential to achieving these progresses. The plans for newly commissioned NSTX-Upgrade will also be discussed.