Isogeometric analysis is a recent technology for numerical simulation, unifying computer aided design (CAD) and computer aided engineering (CAE). It possesses significant advantages over the traditional finite element method. These include the avoidance of mesh generation, exact representation of geometries, higher regularity of the isogeometric discretizations of PDEs, improved accuracy of the obtained numerical solutions, etc. However, it has been noted that these advantages come at the price of constructing spline parameterizations for physical domains and the increased computational cost in the matrix assembly process. This talk will introduce our work on the topics of domain parameterization and matrix assembly in isogeometric analysis.