As we approach the era where we will be able to characterize the atmospheres of terrestrial exoplanets, we are put on a path to answer one of humanity's most compelling questions: are we alone in the universe? Molecular oxygen (O2) with a reducing gas (i.e., methane) is widely regarded as a promising biosignature - a sign of life in the atmospheres of terrestrial exoplanets. However, there are circumstances in which O2 will be very difficult or impossible to detect, such as in atmospheres with small amounts of O2 (as was the case for much of Earth's history), or for missions looking in the mid-IR. For these scenarios, it has been suggested that ozone (O3), the photochemical product of O2, could be used as a proxy to infer the presence of O2. While O3 is not directly produced by life, it plays an important role in habitability as the ozone layer is the primary source of UV shielding for surface life on Earth. However O3 production is known to have a nonlinear dependence on O2, along with being strongly influenced by the UV spectrum of the planet's host star. In this talk I will discuss planetary habitability in general as well as the climate and photochemistry modeling I have done to assess the reliability of O3 as a proxy for O2. Overall I find that the O2-O3 relationship varies significantly around different stellar hosts, with distinct trends between planets orbiting hotter stars (G0V-K2V) versus cooler stars (K5V-M5V). Understanding the full context of the planetary atmosphere will be key for interpreting emission spectral features of biosignature gases.