We draw our attention on the unit sphere in three dimensional Euclidean space. A set X_N of N points on the unit sphere is a spherical t-design if the average value of any polynomial of degree at most t over X_N is equal to the average value of the polynomial over the sphere.The last forty years have witnessed prosperous developments in theory and applications of spherical t-designs. Let integer t>0 be given. The most important question is how to construct a sphericalt-design by minimal N. It is commonly conjectured that N=frac{1}{2}t^2+o(t^2) point exists, but there is no proof. In this talk, we firstly review recent results on numerical construction of spherical t-designs by various of methods: nonlinear equations/interval analysis, variational characterization, nonlinear least squares, optimization on Riemanninan manifolds. Consequently, numerical approximation to singular integral over the sphere by using well conditioned spherical t-designs are also discussed.