When Lorentz symmetry is violated at high energies interactions that are usually non-renormalizable can become renormalizable thanks to a modified power-counting criterion, where space and time are weighted differently. Examples are two-scalar-two-fermion vertices, which can give Majorana masses to left-handed neutrinos without adding extra fields, and four-fermion vertices, which can explain proton decay, if ever observed. There exist renormalizable Lorentz violating Standard Model extensions that agree at low energies with experimental data. If fundamental scalar fields are absent four-fermion vertices trigger a Nambu—Jona-Lasinio mechanism which gives masses to fermions and gauge-bosons and generates composite Higgs fields as low-energy effects. I discuss the phenomenology of these models and argue that present experimental data are compatible with a scale of Lorentz violation well below the Planck scale, possibly as low as 10^14 GeV (assuming that CPT is preserved).