This chapter focuses on the theoretical and computational aspects of biorthogonal wavelets, which extend classical orthogonal wavelets by introducing dual bases for decomposition and reconstruction. The chapter begins with the signal space representation of biorthogonal wavelets, where primal and dual wavelet bases are defined to maintain perfect reconstruction, while allowing greater flexibility in wavelet design. The construction of B-spline wavelets is then discussed, highlighting their smoothness properties and advantages in applications requiring continuous and differentiable functions. The Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet system, derived from B-splines, is introduced as a widely used biorthogonal wavelet family, particularly in image processing. The chapter also explores the lifting scheme, an efficient factorization technique for constructing wavelets with reduced computational complexity.