This thesis focuses on two important topics in astrophysics: the detection of kilonovae (KNe) and gravitationally lensed supernovae (glSNe) in optical surveys. In the first part, the study quantifies the impact of survey depth and choice of filters on the detection probability of KNe. The results highlight the importance of accounting for asymmetries expected for KNe, and despite several search campaigns, no KNe were detected by the Zwicky Transient Facility (ZTF). Nonetheless, non-detection studies provided meaningful constraints on the luminosity function and on the rates of KNe. The findings contribute to advancing our understanding of these rare, fast, and faint transients. I also discuss the improvements in measuring the Hubble constant with follow-up data of KNe, including broadband photometry and spectrophotometric data from the upcoming IFU instrument MAAT. 

The second part of the thesis focuses on gravitationally lensed supernovae. The ZTF survey was expected to detect more than one strongly lensed supernova per year, but only one was identified in the first five years. The study presents simulations of lightcurves for lensed supernovae and new rates based on realistic survey simulations for ZTF. Optimal cuts to distinguish lensed supernovae from normal unlensed supernovae are also provided. The thesis discusses time delay and lightcurve modeling for the one event found during ZTF, SN Zwicky, and the lessons learned from it.

The techniques developed in this thesis can be applied to future surveys to increase the detection rate of KNe and glSNe. These events and their underlying physics provide valuable insights in cosmology.