Signal separation and extraction are important tasks for devices recording audio signals in real environments which, aside from the desired sources, often contain several interfering sources such as background noise or concurrent speakers. Blind Source Separation (BSS) provides a powerful approach to address such problems. However, BSS algorithms typically treat all sources equally and do not resolve uncertainty regarding the ordering of the separated signals at the output of the algorithm, i.e., the outer permutation problem. This paper addresses this problem by incorporating prior knowledge into the adaptation of the demixing filters, e.g., the position of the sources, in a Bayesian framework. We focus here on methods based on Independent Vector Analysis (IVA) as it elegantly and successfully deals with the internal permutation problem. By including a background model, i.e., a model for sources we are not interested to separate, we enable the algorithm to extract the sources of interest in overdetermined and underdetermined scenarios at a low computational complexity. The proposed framework allows to incorporate prior knowledge about the demixing filters in a generic way and unifies several known and newly proposed algorithms using a Bayesian view. For all algorithmic variants, we provide efficient update rules based on the iterative projection principle. The performance of a large variety of representative algorithmic variants, including very recent algorithms, is compared using measured room impulse responses.