The purpose of this review is to focus from an experimental point-of-view on the new physical properties of some of the thinnest superconducting films that can be fabricated and studied in situ nowadays with state-of-the-art methods. An important characteristic of the films we address is that the underlying electronic system forms a two-dimensional electron gas (2DEG). Up to now there are only few of these systems. Such true 2D superconductors can be divided into two classes: surface-confined or interface-confined films. Because the second types of films are burried below the surface, they are not accessible to purely surface-sensitive techniques like angular-resolved photoemission spectroscopy (ARPES) or scanning tunneling spectroscopy (STS). As a consequence the bandstructure characteristics of the 2DEG cannot be probed nor the local superconducting properties. On the other hand, in situ prepared surface-confined films are nowadays accessible not only to ARPES and STS but also to electrical transport measurements. As a consequence surface-confined systems represent at present the best archetypes on which can be summarized the new properties emerging in ultimately thin superconducting films hosting a 2DEG, probed by both macroscopic and microscopic measurement techniques. The model system we will widely refer to consists of a single atomic plane of a conventional superconductor, like for example lead (Pb), grown on top of a semiconducting substrate, like Si(111). In the introductory part 1 we first introduce the topic and give historical insights into this field. Then in the section 2, we introduce useful concepts worked out in studies of so-called 'granular' and 'homogeneous' superconducting thin films that will be necessary to understand the role of non-magnetic disorder on 2DEG superconductors. In this section, we also briefly review the superconducting properties of crystalline Pb/Si(111) ultrathin films grown under ultrahigh vacuum (UHV) conditions in order to illustrate their specific properties related to quantum-size effects. In the next section 3 we review the growth methods and structural properties of the presented 2DEG surface-confined superconductors. In section 4, we review the electronic structure and Fermi surface properties as measured by macroscopic ARPES and confront them to ab initio DFT calculations based on the characterized atomic structures of the monolayers. The following section 5 reviews the macroscopic properties inferred from in situ electrical transport measurements methods, including attempts to study the Berezinsky–Kosterlitz–Thouless 2D regime. In the last section 6, we summarize the emerging local spectroscopic properties measured by STS. These latter demonstrate variations of the local superconducting properties at a scale much shorter than the superconducting coherence length due to a combined effect of non-magnetic disorder and two-dimensionality. Further peculiar local spectroscopic effects are presented giving evidence for the presence of a mixed singlet-triplet superconducting order parameter induced by the presence of a strong Rashba spin–orbit coupling term at the surface. These local signatures will be discussed along with ARPES and transport measurements in parallel high magnetic field on closely related systems. Finally, we present in anisotropic Pb and In monolayers the peculiar role played by atomic steps on vortex properties, leading to the observation by STS of mixed Abrikosov–Josephson vortices in agreement with in situ macroscopic transport measurements. From the overview of all recent experimental and theoretical results it appears that these surface 2D superconductors, such as one monolayer of Pb on Si(111), are ideal templates to engineer and realize topological superconductivity.