I investigate methods for determining black hole accretion rates and star-formation rates in galaxies hosting active galactic nuclei (AGNs) and use these results to identify biases in our census of black hole growth, to probe fundamental differences between obscured and unobscured AGNs, and to explore the connection between black hole growth and galaxy evolution. I show that the mid-infrared [O

IV

] emission line, which probes high-ionization gas and suffers little dust attenuation, is a useful diagnostic of AGN luminosity. Using [O

IV

] measurements for a complete sample of Seyfert galaxies, I show that the intrinsic luminosities of obscured and unobscured AGNs are quite similar. This is in contrast to the [O

III

] optical emission line and hard X-ray continuum luminosities, which are systematically smaller for obscured Seyferts, revealing strong biases in existing AGN surveys. I also explore the effect of AGNs on the mid-infrared aromatic features, which are useful probes of star-formation activity. I find that the 6.2, 7.7, and 8.6 µm features are suppressed relative to the 11.3 µm feature in Seyfert galaxies, and show that this behavior is correlated with the strength of the rotational H₂ emission, which traces shocked gas. This suggests that shocks associated with the AGN modify the structure of aromatic molecules, but I show that the 11.3 µm aromatic feature is robust to the effects of such shock processing, and use it to estimate nuclear star-formation rates for AGN host galaxies. I find an approximately linear relationship between black hole accretion rate and nuclear star-formation rate, and show that high-luminosity AGNs reside in galaxies with more centrally concentrated star formation. This suggests that the strength of AGN activity is driven by the amount of gas in the central few hundred parsecs, and is consistent with models where AGN activity is linked with elevated nuclear star formation.