We present the first continental-scale seismic model of the lithosphere and underlying mantle beneath Southeast Asia obtained from adjoint waveform tomography (often referred to as full-waveform inversion or FWI), using seismic data filtered at periods from 20 - 150s. Based on >3,000h of analyzed waveform data gathered from ~13,000 unique source-receiver pairs, we image isotropic P-wave velocity, radially anisotropic S-wave velocity and density via an iterative non-linear inversion that begins from a 1-D reference model. At each iteration, the full 3-D wavefield is determined through an anelastic Earth, accommodating effects of topography, bathymetry and ocean load. Our data selection aims to maximize sensitivity to deep structure by accounting for body-wave arrivals separately. SASSY21, our final model after 87 iterations, is able to explain true-amplitude data from events and receivers not included in the inversion. The trade-off between inversion parameters is estimated through an analysis of the Hessian-vector product. SASSY21 reveals detailed anomalies down to the mantle transition zone, including multiple subduction zones. The most prominent feature is the (Indo-)Australian plate descending beneath Indonesia, which is imaged as one continuous slab along the 180-degree curvature of the Banda Arc. The tomography confirms the existence of a hole in the slab beneath Mount Tambora and locates a high S-wave velocity zone beneath northern Borneo that may be associated with subduction termination in the mid-late Miocene. A previously undiscovered feature beneath the east coast of Borneo is also revealed, which may be a signature of post-subduction processes, delamination or underthrusting from the formation of Sulawesi.