In this thesis I present a new near-infrared photometric search for unresolved ultracool companions and debris disks to white dwarfs in UKIDSS DR5. 24 DA white dwarfs were found with multiple excesses indicative of a low mass companion, with 7 of these having a predicted mass in the range associated with brown dwarfs. The results of this survey show that the unresolved brown dwarf companion fraction to DA white dwarfs is 0.5 ≤ fWD+BD ≤ 1.8 ± 0.7%. I also calculate the unresolved L-dwarf companion fraction to be 0.5 ≤ fWD+dL ≤ 1.5 ± 0.6%, which is much higher than the previous estimate of Farihi, Becklin & Zuckerman (2005). However, the results are consistent with previous estimates of the brown dwarf companion fraction to main sequence stars.\ud I analyse the near-infrared spectra of eleven known DA white dwarf + M-dwarf binaries, and compare the spectral types assigned using optical photometry against those assigned using near-infrared spectra. I search for evidence that the known short period systems once existed in a common envelope phase. No such evidence was found.\ud I also present the spectroscopic analysis of two particularly interesting binaries; PG 1234+ 482 and PHL 5038. PG 1234+482 is the hottest and youngest DA white dwarf with a cool companion on the stellar-substellar borderline. I discuss the possibility that the companion is a brown dwarf, and the possibility that the secondary is the source of contamination by heavy metals in the white dwarf's atmosphere. PHL 5038 was identified to have a near-infrared excess in UKIDSS, and the spectroscopic analysis in this thesis confirms that the secondary in this system can be resolved at a projected orbital separation of 55AU, and is a brown dwarf with spectral type L8-L9. This is only the second such pair found (over 20 years later) after GD165AB. The secondary in this system has the potential to be used as a benchmark brown dwarf for testing substellar atmospheric models
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