What are the current observational constraints on the existence of Nemesis? Nemesis is a hypothetical companion to the Sun on a very eccentric, long-period orbit. The star supposedly returns every few tens of millions years, driving comets into the inner solar system and causing extinction events. Given our very stringent observational limits from infrared surveys (such as WISE), is its existence definitively ruled out?
Few important points about WISE:


it was able to detect anything with a temperature above 70-100 K, whereas the coolest brown dwarfs are in the 500-600 K range (the coolest was discovered by WISE itself, see Mainzner et al., 2011);
it was able to detect objects larger than 1km up to 3 AU from the Sun, or objects of 2-3 Jupiter masses in a distance up to 7-10 light-years (see here and here);
the closest brown dwarf detected by WISE is a brown dwarfs binary system, located at 6.6 light-years from the Sun.


So I would say we can be pretty confident that Nemesis existence has been ruled out.