Statistical dialogue management is the core of cognitive spoken dialogue systems (SDS) and has attracted great research interest. In recent years, SDS with the ability of evolution is of particular interest and becomes the cuttingedge of SDS research. Dialogue state tracking (DST) is a process to estimate the distribution of the dialogue states at each dialogue turn, given the previous interaction history. It plays an important role in statistical dialogue management. To provide a common testbed for advancing the research of DST, international DST challenges (DSTC) have been organised and well-attended by major SDS groups in the world. This paper reviews recent progresses on rule-based and statistical approaches during the challenges. In particular, this paper is focused on evolvable DST approaches for dialogue domain extension. The two primary aspects for evolution, semantic parsing and tracker, are discussed. Semantic enhancement and a DST framework which bridges rule-based and statistical models are introduced in detail. By effectively incorporating prior knowledge of dialogue state transition and the ability of being data-driven, the new framework supports reliable domain extension with little data and can continuously improve with more data available. Thismakes it excellent candidate for DST evolution. Experiments show that the evolvable DST approaches can achieve the state-of-the-art performance and outperform all previously submitted trackers in the third DSTC.