Inclusion Criteria:  Adult patients with confirmed diagnosis of relapsed/refractory B-cell NHL with all subtypes of DLBCL, follicular lymphoma (FL), marginal zone lymphoma (MZL) and mantle cell lymphoma (MCL) per WHO 2016 criteria. Patients in subtype arm e.g. DLBCL must have confirmed diagnosis of relapsed/refractory DLBCL. Received and failed or be intolerant to standard of care therapy (at least two prior lines, including an anti-CD20 therapy, but no more than 5 prior lines) Must have measurable disease and ECOG of 0 to 2 Must have a site of disease amenable to biopsy and be a candidate for tumor biopsy and be willing to undergo study required biopsies at screening and during therapy  Exclusion Criteria:  Baseline laboratory results outside of protocol defined ranges Presence of history of central nervous system involvement by lymphoma History of hypersensitivity to VAY736 or any drugs in similar chemical classes (e.g. monoclonal antibodies) Impaired cardiac function or clinically significant cardiac disease History of or current interstitial lung disease or pneumonitis grade 2 or higher HIV infection Active hepatitis C infection and/or hepatitis B infection Pregnant or nursing (lactating) women Women of child-bearing potential unless they are using highly effective methods of contraception  Other Inclusion/Exclusion criteria may apply