The early observation at HERA of an excess of events compared to the expectation from the Standard Model in very short distance $e^+p$ deep-inelastic scattering processes has renewed the interest in the search for new physics which could manifest in electroweak-like interactions. New preliminary results from the H1 and ZEUS experiments making use of all available $e^+p$ data are reviewed here, with an emphasis on the search for new bosons possessing Yukawa couplings to lepton-quark pairs. The sensitivity of HERA to leptoquarks, and to squarks of R-parity violating supersymmetry, is confronted to existing indirect constraints from rare and forbidden semi-leptonic decays, atomic parity violation and neutrinoless double-beta decay, as well as to direct constraints from LEP and Tevatron colliders. The HERA and Tevatron colliders are found to offer exciting prospects for new physics, accessing yet unexplored domains of the mass-coupling plane. Possible striking manifestation of explicit lepton flavour violation is also discussed.