Ion mobility separations have emerged as a major tool for mass spectrometry of proteins and peptides. The high speed of ion mobility spectrometry (IMS) compared with chromatography enables accelerating proteomic analyses at same separation power or raising the peak capacity at equal throughput. Of interest to structural biology, tractable physics of ion transport in gases permits characterizing the structure of macromolecules by matching measured mobilities to values calculated for candidate geometries. The two known experimental methods are drift-tube IMS based on absolute mobility and field asymmetric waveform IMS (FAIMS) based on differential mobility as a function of electric field. Here, we describe combining them into 2D separations coupled to time-of-flight MS, a development made practical by electrodynamic ion funnel interfaces that effectively convey ions in and out of IMS, including "hourglass" funnels to accumulate ions filtered by FAIMS between pulsed injections into IMS. For peptide separations, the peak capacity of FAIMS/IMS is ~500 and potentially higher, a metric close to that of top capillary LC systems. In structural investigations, FAIMS/IMS allows more protein conformers to be distinguished than either stage alone, and extends the dynamic range of detection by an order of magnitude over 1D IMS. A controlled heating of ions by rf field over a variable time in the funnel trap between FAIMS and IMS stages allows following the evolution of selected isomers in both thermodynamic and kinetic aspects, which opens a new approach to mapping the pathways and energy surfaces of protein folding.