Batch proofs are interactive proof systems that allow a prover to convince a verifier that multiple inputs belong to a language in NP with significantly less communication than sending individual witnesses. This work explores the limitations and possibilities of batch proofs, focusing on statistical and computational soundness. The authors show that statistically sound batch proofs for a language L imply that L has a statistically witness-indistinguishable (SWI) proof with inverse polynomial error and a non-uniform honest prover. This result is unconditional for obtaining honest-verifier SWI or full-fledged SWI from public-coin protocols, but requires one-way functions for private-coin protocols. This poses a barrier for achieving batch proofs beyond UP, where witness indistinguishability is trivial. Assuming NP does not have SWI proofs, batch proofs for all of NP do not exist. For computationally sound batch proofs (BARGs), the authors show that assuming one-way functions, they imply statistical zero-knowledge (SZK) arguments for NP with roughly the same number of rounds, inverse polynomial error, and non-uniform honest prover. This would be surprising as SZK arguments are currently only known under constant-round statistically-hiding commitments. The authors also prove new positive implications of non-interactive batch arguments to non-interactive zero-knowledge arguments (with explicit uniform prover and verifier). They introduce a new framework that transforms a batch protocol for a language L into an SWI protocol for L. This framework is used to derive barriers and positive results for batch proofs and arguments. The work shows that non-interactive BARGs for NP, together with one-way functions, imply non-interactive computational zero-knowledge arguments for NP. Assuming dual-mode commitments, the zero knowledge can be made statistical. The authors also show that lossy public-key encryption can be derived from somewhere extractable BARGs. The results highlight the limitations of batch proofs and the importance of cryptographic assumptions in achieving efficient and secure protocols. The work contributes to the understanding of the relationship between batch proofs, witness indistinguishability, and zero-knowledge arguments in cryptography.Batch proofs are interactive proof systems that allow a prover to convince a verifier that multiple inputs belong to a language in NP with significantly less communication than sending individual witnesses. This work explores the limitations and possibilities of batch proofs, focusing on statistical and computational soundness. The authors show that statistically sound batch proofs for a language L imply that L has a statistically witness-indistinguishable (SWI) proof with inverse polynomial error and a non-uniform honest prover. This result is unconditional for obtaining honest-verifier SWI or full-fledged SWI from public-coin protocols, but requires one-way functions for private-coin protocols. This poses a barrier for achieving batch proofs beyond UP, where witness indistinguishability is trivial. Assuming NP does not have SWI proofs, batch proofs for all of NP do not exist. For computationally sound batch proofs (BARGs), the authors show that assuming one-way functions, they imply statistical zero-knowledge (SZK) arguments for NP with roughly the same number of rounds, inverse polynomial error, and non-uniform honest prover. This would be surprising as SZK arguments are currently only known under constant-round statistically-hiding commitments. The authors also prove new positive implications of non-interactive batch arguments to non-interactive zero-knowledge arguments (with explicit uniform prover and verifier). They introduce a new framework that transforms a batch protocol for a language L into an SWI protocol for L. This framework is used to derive barriers and positive results for batch proofs and arguments. The work shows that non-interactive BARGs for NP, together with one-way functions, imply non-interactive computational zero-knowledge arguments for NP. Assuming dual-mode commitments, the zero knowledge can be made statistical. The authors also show that lossy public-key encryption can be derived from somewhere extractable BARGs. The results highlight the limitations of batch proofs and the importance of cryptographic assumptions in achieving efficient and secure protocols. The work contributes to the understanding of the relationship between batch proofs, witness indistinguishability, and zero-knowledge arguments in cryptography.