State-of-the-art axisymmetric drop shape analysis (ADSA) techniques for the computation of interfacial tensions and contact angles by fitting the Laplace equation of capillarity to the shape and dimensions of pendant and sessile drops are presented. More accurate, efficient, and reliable versions of the technique for the measurement of contact angles from the volume and diameter of sessile drops [axisymmetric drop shape analysis-diameter (ADSA-D)] and for interfacial tension measurements from a series of arbitrary profile coordinates of sessile and pendant drops [axisymmetric drop shape analysis-profile (ADSA-P)] have been developed. Advanced numerical methods have been used to improve the numerical stability and global convergence, for more accurate results and a wider range of applicability of the methods. A new technique called axisymmetric drop shape analysis-height and diameter (ADSA-HD) has been developed to estimate interfacial tensions from the height and diameter of sessile and pendant drops. Numerical simulations using numerically generated drop profiles were used to evaluate the accuracy and applicability of the methods.