Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications, We initiate the study of agnostic process tomography: given query access to an unknown quantum channel Φ and a known concept class C of channels, output a quantum channel that approximates Φ as well as any channel in the concept class C, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by QAC0 circuits. I will give an overview of our results and approach as well as potential applicants of such learning tools in cryptography.