In this paper we present a comprehensive discussion of a new class of inline microwave filters with transmission zeros in the response, namely the path filters. The main features of this filters class are highlighted, and an original (synthesis-based) design approach is presented, relying on the derivation of suitable characteristic polynomials. In addition to the classical Generalized Chebyshev characteristic, two new characteristics are introduced (namely the Bounded Chebyshev and the Reduced Chebyshev), that allow improving the flexibility in the requirements assignment of path filters. A new method for the synthesis of the lowpass prototype is also introduced, that overcome the limitation in the classical synthesis based on the manipulation of the transversal prototype (whose synthesis may fail in case of path filters). Finally, the proposed approach for designing the class of considered filters has been validated by several examples that include the evaluation of the characteristic polynomials, the prototype synthesis and the dimensioning of the physical structures in waveguide technology.