Landlords are responsible for keeping apartments livable and fixing structural issues like a leaky roof, as well as keeping plumbing, electricity and other systems safely operational.
They probably aren't responsible for cosmetic repairs, such as peeling paint, but generally do pay for the cost of any pest control or extermination services, according to Nolo.
The main exception occurs when a tenant may be responsible for the problem, so if they leave food out all the time and pests come in, they may have to pay. If one has mistreated the property in some way and is responsible for repair costs but does not pay, the money may be taken out of that tenant's security deposit.
Nolo notes that beyond the major concerns, the responsibility can vary. It's a good idea to check state laws concerning landlords and tenants, and any state or local building codes that address the issue. Property lease documents may clarify responsibilities as well.
A landlord may be more likely to fix a problem that may cause an injury or further damage to the property, since those can lead to greater expenses later. Filing a request for repair which outlines not only the reasons you want something fixed, but also reasons the landlord should want to fix it may help.