jats:p Industrial, academic, activist, and policy research and advocacy movements formed around resisting ‘machine bias’, promoting ‘ethical AI’, and ‘fair ML’ have discursive implications for what constitutes harm, and what resistance to algorithmic influence itself means, and is deeply connected to which actors makes epistemic claims about harm and resistance. We present a loose categorization of kinds of resistance to algorithmic systems: a dominant mode of resistance as ‘filtering up’ and being translated into design fixes by Big Tech; and advocacy and scholarship which bring a critical frame of lived experiences and scholarship around algorithmic systems as socio-technical entities. Three recent cases delve into how Big Tech responds to harms documented by marginalized groups; these highlight how harms are valued differently. Finally, we identify modes of refusal that recognize the limits of Big Tech's resistance; built on practices of feminist organizing, decoloniality, and New-Luddism, they encourage a rethinking of the place and value of technologies in mediating human social and personal life; and not just how they can deterministically ‘improve’ social relations. </jats:p>