  Future large-scale structure surveys will measure three-point statistics with
high statistical significance. This will offer significant improvements on our
understanding of gravity, provided we can model these statistics accurately. We
assess the performance of several schemes for theoretical modelling of the
matter bispectrum, including halo-model based approaches and fitting formulae.
We compare the model predictions against N-body simulations, considering scales
up to $k_{\rm max} = 4 h/{\rm Mpc}$, well into non-linear regime of structure
formation. Focusing on the equilateral configuration, we conduct this analysis
for three theories of gravity: general relativity, $f(R)$ gravity, and the DGP
braneworld model. Additionally, we compute the lensing convergence bispectrum
for these models. We find that all current modelling prescriptions in modified
gravity, in particular for theories with scale-dependent linear growth, fail to
attain the accuracy required by the precision of the Stage IV surveys such as
\emph{Euclid}. Among these models, we find that a halo-model corrected fitting
formula achieves the best overall performance.
