In this talk, we first review the background of algebraic hyperkähler metrics with asymptotic behavior and twistor spaces, and introduce a complex manifold called the principal twistor model (PTM). We then present the main theorem on the universality of the PTM and its application to the moduli space. The universality of the PTM is as follows: Let X be a conical symplectic variety admitting a crepant resolution Y. If the regular locus of X admits a hyperkähler cone metric g_0, then the twistor space of any algebraic hyperkähler metric g on Y asymptotic to g_0 is uniquely recovered by slicing the PTM. In the second half of the talk, we construct the PTM based on the theory of universal Poisson deformations and explain the proof of its universality.