This paper first presents the fundamental principles of the microwave photonic filters. As an example to explain how to implement a microwave photonic filter, a specific finite impulse response (FIR) filter is illustrated. Next, the Q value of the microwave photonic filters is analyzed theoretically, and methods around how to gain high Q value are discussed. Then, divided into FIR filter, first-order infinite impulse response (IIR) filter, and multi-order IIR filter, several novel microwave photonic filters with high Q value are listed and compared. The technical difficulties to get high Q value in first-order IIR filter and multi-order IIR filter are analyzed concretely. Finally, in order to gain higher Q value, a multi-order IIR microwave photonic filter that easily extends its order is presented and discussed.