Three searches are presented for long-lived particles with specific production and decay features: pairs of long-lived particles from Higgs boson decay and decaying either to jet pairs or to three quarks, and long-lived particles decaying semileptonically. The searches use proton-proton collision data corresponding to integrated luminosities up to 3.0$\,$fb$^{−1}$, collected by the LHCb detector at centre-of-mass energies of 7 and 8$\,$TeV. All three searches observed no excess above background and set limits on the production cross-sections as a function of the mass and lifetime of the long-lived particles.