In this talk we will review some obstacle-type problems and their applications. Particular focus will be given to the thin obstacle problem which in some instances is the same as the so-called Signorini problem which has applications in biology and finance. We will then formulate the two-phase parabolic Signorini problem which has its own applications. We will show how the two phases in this problem cannot touch. This separation of the phases leads to a proof of the optimal regularity of the solution.