A brief survey of the recent experimental and theoretical results on the low threshold distributed feedback (DFB) lasing in chiral liquid crystals (CLC) as well as new original theoretical results in the field are presented. The presentation is concentrated on the lasing thresholds at frequencies corresponding to the stop band edge lasing modes and defect modes in CLC. It is demonstrated that the analytic approach reproduces all features of the DFB lasing in CLC obtained by the traditional numerical approach and, more over, allows to reveal some qualitative effects escaped from the researchers employing the numerical methods. Namely, the effect of anomalously strong absorption at the defect mode frequency, a direct analogue of the corresponding effect at the stop band edge mode frequency, is predicted in the framework of the analytic approach. It is proposed also to reduce the lasing threshold by adjusting the pumping wave to the conditions of the anomalously strong absorption effect at the defect mode frequency. The developed approach helps to clarify the physics of lasing at the stop band edge and defect modes in CLC and manifests an agreement with the corresponding results of the previous investigations obtained by a numerical approach.