The present disclosure provides methods, compositions, kits and systems for nucleic acid amplification. In some embodiments, nucleic acid amplification methods include subjecting the nucleic acid to be amplified to partially denaturing conditions. In some embodiments, nucleic acid amplification methods include amplifying without fully denaturing the nucleic acid that is amplified. In some embodiments, the nucleic acid amplification method employs an enzyme that catalyzes homologous recombination and a polymerase. In some embodiments, methods for nucleic acid amplification can be conducted in a single reaction vessel and/or in a single continuous liquid phase of a reaction mixture, without need for compartmentalization of the reaction mixture or immobilization of reaction components. In some embodiments, methods for nucleic acid amplification comprise amplifying at least one polynucleotide onto a surface under isothermal amplification conditions, optionally in the presence of a polymer which can include a sieving agent and/or a diffusion-reducing agent.