A process of forming a soft and resilient web exhibiting a substantially continuous pattern of debossments or apertures is disclosed. The process comprises locally heating process to melt predetermined points of the web. The process includes: continuously bringing the web in contact relation with a forming structure exhibiting a substantially continuous pattern of apertures corresponding to the debossments or apertures of the web; locally heating the region of the web at the predetermined points along the surface of the web by an energy source to give the web temperature above its melting temperature; applying a substantially uniform fluid pressure differential to the locally heated web at least in those areas to be debossed or apertured, whereby the web is debossed or apertured at the predetermined points and generally maintains its surface structure at least in those areas in which the web is not debossed or apertured; and removing the debossed or apertured web from the forming structure. A soft and resilient web formed by the process is also disclosed.