Helical fermi liquids (HLFL) have momentum dependent spin or pseudospin alignments at the fermi surface, the simplest example is the edge states of
topological band insulator. We study quantum phase transitions associated with spontaneous time-reversal, space inversion, and spin-spatial rotation symmetry
breakings in HLFL. Due to the special spin alignment of HLFL at the fermi surface, part of the quantum critical modes decouple from the particle-hole
excitation in the infrared limit, hence the universality class and quasiparticle behavior at the transition in general differ from the standard Hertz-Millis theory. Application of our results to other systems such as iron-pnictides superconductor, and the bulk states of strong topological insulator will also be discussed.