Abstract: In the scheme of electron-driven fast ignition of inertial confinement fusion (ICF), MeV relativistic electron beams driven by ultraintense petawatt laser pulses are required and electron energy of several tens of kilojoules should be deposited in the compressed core of an imploded DT shell. The beam quality is crucial to the success of fast ignitor. In order to study the generation and transport of the relativistic electron beam, a three-dimensional high-performance parallel particle-in-cell code is developed and improved. In this review, this paper shows the researches on the generation of high-quality electron beams and the method of beam divergence controlling of our research group. Two main reasons for poor beam quality are firstly introduced: pre-plasma effect and random scattering of the magnetic field produced by the beam instability. In addition, enhancement of electron beam flux and collimation of its propagation are investigated. Four ways to obtain collimated electrons are put forward: 1) reduce the pre-plasma effect with a double cone target; 2) collimate fast electrons in specially engineered targets with the spontaneously generated magnetic field during its transportation; 3) collimate fast electrons with external magnetic field; 4) control the beam instability at the laser-plasma interface.