The paper presents results of theoretical investigations of processes of excitation of microwave electromagnetic radiation during stimulated scattering of Langmuir waves on relativistic electron beam (free electron plasma laser). Physical models are considered for infinite and bounded plasma (plasma wave-guide). The linear and non-linear theory of stimulated scattering of Langmuir waves on REB is investigated. The effects of focusing of microwave radiation in free electron plasma lasers are inspected. The stimulated scattering of plasma wave on REB in periodical non-gomogenous plasma is considered.