Although the LHC experiments have searched for and excluded many proposed new particles up to masses close to 1 TeV, there are many scenarios that are difficult to address at a hadron collider.
This talk will review a number of these scenarios and present the expectations for searches at an electron-positron collider such as the International Linear Collider.
The cases discussed include SUSY in strongly or moderately compressed models, heavy neutrinos, heavy vector bosons coupling to the s-channel in $e^+e^-$ annihilation, and new scalars.