Solid solutions of III-V semiconductor with bismuth are theoretically predicted to host topologically protected surface states due to the inversion of electronic bands at sufficiently high Bi content. Partial replacement of As, or Sb anions with Bi heavy element in the III-V host leads to considerable bandgap reduction in the range of 40 - 60 meV per 1% of Bi depending on the III-V material, but theoretically predicted band inversion has not been experimentally observed yet. I will present selected results related to molecular beam epitaxy grown Ga(As,Bi) both in native cubic (zinc blende) and hexagonal (wurtzite) phase, as well as In(As,Bi) with Bi content of up to 100% (i.e. including InBi binary compound) in view of expected and observed topological properties.