Solar-induced fluorescence (SIF) is a subtle but informative optical signal of vegetation photosynthesis. Remotely sensed SIF integrates environmental, physiological and structural changes that alter photosynthesis at leaf, plant and canopy scales. Radiative transfer models are ideally suited to investigate the complex sources of variability in the SIF signal to guide the interpretation of SIF retrievals from airborne and space-borne platforms. Here, we coupled the Fluspect-Cx model of leaf optical properties and chlorophyll-a fluorescence with the Discrete Anisotropic Radiative Transfer (DART) model to upscale SIF from individual leaves to three-dimensional (3D) structurally explicit canopies. For one-dimensional homogeneous (turbid-like) canopies, DART-SIF was nearly identical to SIF simulated in two existing models, SCOPE and mSCOPE (RMSE <0.221 W.m−2.μm−1.sr−1). DART simulations in geometrically explicit 3D canopies offered four important insights regarding the influence of vegetation structure on the multi-angular top-of-canopy SIF signal. First, changes in the 3D canopy architecture of maize crops, represented by leaf density (leaf area index), and plant clumping (canopy closure) had a larger impact on SIF than the modelled photosynthetic efficiency distinction between sun-adapted and shade-adapted foliage. Second, clumping of leaves at the crop and stand levels was identified as one of the key driving factors of multi-angular anisotropy of red and far-red SIF (686 and 740 nm) for both maize and eucalyptus canopies. Third, non-photosynthetic woody material had a significant impact on top-of-canopy SIF in modelled 3D forest stands. Wood shadowing decreased the photosynthetically active radiation absorbed by green leaves, and consequently the SIF emissions, by 10% in sparse and 17% in dense eucalyptus stands. The wood obstruction (blocking) effect, quantified as a relative difference of SIF escape probabilities from canopies with and without wood in the nadir viewing direction, decreased far-red SIF by 4–6% but it had a smaller and sometimes positive influence (by less than 2%) on red SIF. Fourth, DART 3D radiative budget profiles revealed that the majority of the SIF signal from a dense eucalyptus stand originated from the top 25% of the simulated canopy. Interestingly, the introduction of bark-covered woody elements did not alter the simulated balance and omnidirectional escape factor of red SIF in this upper canopy part but did raise significantly both of them in case of far-red SIF. These results demonstrate the importance of 3D radiative transfer and radiative budget simulations for investigating SIF interactions in structurally complex plant canopies and for a better understanding of spatiotemporal and multi-angular remote sensing SIF observations.