Polymers have appealing optical, biochemical, and mechanical qualities, including broadband transparency, ease of functionalization, and biocompatibility. However, their low refractive indices have precluded wavelength-scale optical confinement and nanophotonic applications in polymers. Here, we introduce a suspended polymer photonic crystal (SPPC) architecture that enables the implementation of nanophotonic structures typically limited to high-index materials. Using the SPPC platform, we demonstrate nanophotonic band-edge filters, waveguides, and nanocavities featuring quality (Q) factors exceeding 2, 300 and mode volumes (V(mode)) below 1.7(λ/n)(3). The unprecedentedly high Q/V(mode) ratio results in a spectrally selective enhancement of radiative transitions of embedded emitters via the cavity Purcell effect with an enhancement factor exceeding 100. Moreover, the SPPC architecture allows straightforward integration of nanophotonic networks, shown here by a waveguide-coupled cavity drop filter with sub-nanometer spectral resolution. The nanoscale optical confinement in polymer promises new applications ranging from optical communications to organic opto-electronics, and nanophotonic polymer sensors.