This chapter introduces a powerful framework for quantum algorithms: qubitization and quantum signal processing. The qubitization method is derived to demonstrate the application of Chebyshev polynomials of block-encoded matrices and their sums to quantum states. The quantum signal processing theorem is then stated as a more efficient method to apply polynomials of block-encoded matrices. Finally, the quantum eigenvalue transform and quantum singular value transform are presented, which underpin modern simulation and linear algebra algorithms.