Starting with Feynman's "There's Plenty of Room at the Bottom" prophetic lecture at Caltech in the 1960s, the term "nanotechnology" was first coined in the scientific literature in the 1980s. This was followed by the unprecedented growth in the corresponding scientific field in 2000 due to the financial incentive provided by President Clinton in the US, followed up by similar efforts in Europe, Japan, China and Russia. Today, nanotechnology has become a driving force for economic development, with applications in all fields of engineering, information technology, transport and energy, as well as biology and medicine. Thus, it is important to forecast its future growth and evolution on the basis of two different criteria: (1) the government and private capital invested in related activities, and (2) the number of scientific publications and popular articles dedicated to this field. This article aims to extract forecasts on the evolution of nanotechnology, using the standard logistic equation that result in familiar sigmoid curves, as well as to explore the effect of time delay on its evolution. Time delay is commonly known from previous biological and ecological models, in which time lag is either already known or can be experimentally measured. In contrast, in the case of a new technology, we must first define the method for determining time delay and then interpret its existence and role. Then we describe the implications that time delay may have on the stability of the sigmoidal behavior of nanotechnology evolution and on the related oscillations that may appear.