Studies of the gas phase structures of biomolecules provide an important connection to theoretical methods for modeling large molecular structures. The key features of biomolecule structures, such as their conformational flexibility and the complexes they form through intermolecular interactions, pose major challenges to spectroscopic techniques. Rotationally resolved spectroscopy holds the possibility of true structure determination where analysis of the spectra of isotopic species provides actual atom positions in the three-dimensional structure. Molecular rotational spectroscopy is ideally suited for this type of study because it offers high spectral resolution and is generally applicable (requiring only a polar molecule). A chirped-pulse Fourier transform microwave (CP-FTMW) spectrometer has been optimized for biomolecular spectroscopy. The sensitivity of this technique makes it possible to perform heavy atom (13C, 15N, 18O) structure determination using the natural abundance of the isotopes. The performance of the spectrometer is illustrated by obtaining the structure of the phenol dimer, a model system that is a challenge for theoretical methods. For application to larger biomolecule systems, it is expected that rotational spectroscopy alone will face challenges in making structural determinations. The scope of problems that can be addressed by rotational spectroscopy can be expanded through double-resonance spectroscopy approaches that provide a "second dimension" of structural information. A general method to implement laser-microwave double resonance spectroscopy is described. We also discuss the potential for developing low-cost microwave detectors for biomolecular spectroscopy that achieve savings by reducing the measurement bandwidth. This approach is particularly promising for developing low-frequency CP-FTMW spectrometers that are well-suited for large molecule rotational spectroscopy.