A basic problem in knot theory is how to classify knots. After the Jones discovery of new polynomial invariants of knots in 1984, various kinds of knot invariants were obtained by many mathematicians and then there arose a problem of organising these invariants.
In 1990, V. A. Vassiliev introduced finite type invariants of knots and many mathematicians get fruitful results based on the theory. But still there is a famous probelm, whether Vassiliev invariants distinguish all knots or not. This problem is proved to be equivalent to the problem whether the similarity indices of all pairs of two different knots are finite or not. In this talk, we introduce some methods to estimate the similarity indices of knots, links and tangles by using Vassiliev invariants and subtangles.