This thesis applies the one-dimensional (1-D) and two-dimensional (2-D) cubic-spline interpolation (CSI) schemes to MPEG standard for very low-bit rate video coding. In addition, the CSI scheme is used to implement the scalable video compression scheme in this thesis. The CSI scheme is based on the least-squares method with a cubic convolution function. It has been shown that the CSI scheme yields a very accurate algorithm for smoothing and obtains a better quality of reconstructed image than linear interpolation, linear-spline interpolation, cubic convolution interpolation, and cubic B-spline interpolation. In order to obtain a very low-bit rate video, the CSI scheme is used along with the MPEG-1 standard for video coding. Computer simulations show that this modified MPEG not only avoids the blocking effect caused by MPEG at high compression ratio but also gets a very low-bit rate video coding scheme that still maintains a reasonable video quality. Finally, the CSI scheme is also used to achieve the scalable video compression. This new scalable video compression scheme allows the data rate to be dynamically changed by the CSI scheme, which is very useful when operates under communication networks with different transmission capacities.