In this work, a likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on a soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma gives alternative achievability proofs for classical source coding problems. The case of the rate-distortion function with side information at the decoder (i.e. the Wyner-Ziv problem) is carefully examined and an application of the likelihood encoder to the multi-terminal source coding inner bound (i.e. the Berger-Tung region) is outlined.