In recent years, preceded by decisive advances in multi-TW laser technolgy a breakthrough was achieved in the field of laser-based electron acceleration. In the so-called wakefield or bubble acceleration regime, using a high-intensity laser pulse electrons from an underdense plasma can be accelerated to quasi-monoenergetic energy distributions over distances between several mm and cm, with the spectrum’s quasi-monoenergetic peak being able to reach energies of more than 1 GeV. This compact way of laser-based electron acceleration is of great interest for numerous applications, e.g. generating pulsed variable-wavelength secondary radiation, not least because of the extremely short duration of the electron pulse, which is on the order of femtoseconds. HI-Jena pursues research in laser electron acceleration with several laser systems. The major goal is to understand the underlying acceleration mechanisms more completely, and to optimize the electron pulse parameters with regard to possible future applications.