Rapidly spinning, non-axisymmetric neutron stars are expected to emit long-lived, quasi-monochromatic gravitational-wave (GW) signals in the observing band of current ground-based GW detectors. These continuous gravitational waves (CWs) have thus far gone undetected, but a first CW detection promises novel insights into the physics of neutron star interiors and ultra-dense nuclear matter. I will discuss data analysis techniques used to search for these elusive signals, and highlight several challenges that CW analysts must contend with. Of these challenges, I will focus on narrowband spectral noise artifacts, appearing as “lines” in GW detector spectra, and will discuss efforts to both characterize and catalog these artifacts.