We review some advances relating to direct N-body codes. In particular, there has been significant progress in dealing with large-N systems containing a few dominant members. The simulation of massive black holes also requires treatment of relativistic effects for strongly bound two-body orbits. Although somewhat costly, the addition of post-Newtonian terms is still straightforward when used in connection with regularization methods. Several versions of multiple regularization are especially well suited to studying black hole problems. We also report on a new stability criterion for the general three-body problem which will provide a robust test in systems where hierarchies are a troublesome feature, as in the case of star cluster simulations with primordial binaries.

Until a few years ago, the common paradigm for the formation of Globular Clusters (GCs) was that they constitute a ‘simple stellar population’ in which all the stars were formed from a chemically homogeneous cluster medium within a relatively short interval of time, at the beginning of the galactic life. In recent years, the spectroscopic information on the low luminosity (turnoff) cluster stars have extended to the unevolved stars the recognition that chemical anomalies are a common feature of GCs and not an exception. This has provoked a revolution in the simple view of GC formation, and requires an adequate dynamical modelling including gas dynamics. It is by now well accepted that at least two different stellar components are common in most GCs. These are almost unequivocally identified with (i) a first stellar generation, which gave origin to stars of all masses; and (ii)) a second generation, born from the ejecta of the most massive asymptotic giant branch stars of the first generation, in the first 100–200 Myr from the first burst of star formation. A ‘third’ population is present only in some GCs, and is more difficult to be understood. It is characterized by stars having a huge helium content (Y ≃ 0.4, if stellar modelling is reasonable) and extreme chemical anomalies in the proton capture elements (Na, O, Al). The status of understanding of the GC properties, based on our most recent models of stellar evolution, is discussed.

In dense stellar systems, dynamical interactions between objects inevitably lead to frequent formation of exotic stellar objects and multiple systems, thereby imposing new questions for the stellar evolution theory. The evolutionary path of such systems could be different from that of the unperturbed objects, therefore, we must re-evaluate their evolutionary treatment to clarify their consequent dynamical evolution. We review briefly the classes of important dynamical encounters and discuss several post-encounter outcomes that may require more detailed attention or development of a new treatment in stellar evolution: evolution of complex merger products, spun-up stars, binaries with stripped giants and triples.

I briefly present the most relevant observational facts supporting the idea of one or more star formation episodes in globular clusters.

We investigate some implications of having two star formation episodes in globular clusters, rather than the traditional single-burst approximation. Evidence for more than one stellar generation is accumulating in observations of abundances of elements lighter than iron in globular cluster stars, and is thought to imply some self-enrichment of the globular cluster gas. In particular, we explore models based on the assumption that the self-enrichment comes from an early generation of asymptotic giant branch (AGB) stars.

Blue stragglers stars (BSS) define a sparsely populated sequence extending to higher luminosity than the turnoff point of normal main sequence stars in the color magnitude diagrams of stellar aggregates, thus mimicking a rejuvenated (more massive) stellar population. The nature of these stars has been a puzzle for many years and their formation mechanism is not completely understood, yet. Two mechanisms have been proposed to produce BSS: (i) the mass transfer in binary systems; and ((ii) the merger of two stars induced by stellar interactions. In this contribution we schematically report on the main properties of BSS in globular clusters (GCs) in the light of the most recent photometric and spectroscopic observations. These results, combined with dynamical simulations, indicate that both the proposed formation mechanisms play an important role in the production of BSS in GCs.

The formation of special binaries in a globular cluster is regulated by the total encounter rate γ in the cluster, but their life expectancy by the number of encounters γ that one system experiences. The orbital periods indicate whether a neutron star or white dwarf entered a binary via direct collision, via tidal capture, or via exchange encounter. The numbers of X-ray binaries with a neutron star scales with γ. Magnetically active binaries (including blue stragglers) are formed via evolution of primordial binaries, and their numbers scale with the cluster mass. Cataclysmic variables are formed by stellar encounters or via evolution of a primordial binary in clusters with high and low central density, respectively.

The old open cluster M 67 is an ideal test case for current star cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here we discuss a direct N-body model of M 67. This model of 12,000 single stars and 12,000 binaries is evolved from zero-age and takes full account of cluster dynamics as well as stellar and binary evolution. At an age of 4 Gyr the model cluster matches the mass and structure of M 67 as constrained by observations. We discuss the role of the primordial binary population and the cluster environment in shaping the nature of the stellar populations of M 67, with a focus on X-ray binaries and blue stragglers.

We summarize the characteristics of 85 spectroscopic orbits derived from more than two decades of radial-velocity monitoring of stars in the old open cluster M 67, with special emphasis on the blue stragglers and other members that do not fall on the evolutionary tracks expected for isolated single stars.

In preparation for the first simulation of a real globular cluster with a few 105 particles and several Gyr of evolution, which will be made possible by the advent of the new GRAPE-8, the MODEST community encharged our working group (WG-9) to provide all of the needed observational constrains. The selected clusters for this experiment were NGC 6121 (M 4) and NGC 6397. We present the status of the project.

Modelling rich star clusters is at an exciting time, now that detailed star-by-star modelling of all open star clusters has become possible. We should renew attention to the modelling of globular star clusters, to enable us to exploit the flood of excellent observational data now available. At the same time, new ideas in star cluster astrophysics require us to broaden the realism of our modelling in various directions.

We present and discuss recent new results from the Spitzer Space Telescope and their impact on cosmology.

The IAU Joint Discussion 16 was held at the IAU XXVI General Assembly in Prague, in August 2006. The title of the meeting was Nomenclature, Precession and new models in Fundamental Astronomy. Applications and scientific contribution to astronomy. It was organized by IAU Division I (Fundamental Astronomy) and Commission 19 (Earth Rotation), with the participation of IAU Division, X (Radio Astronomy) and all the Division, I Commissions, as well as with the support of the International Association of Geodesy (IAG). The Scientific Organizing Committee was made up of the three organizers and the representatives of these scientific bodies.

We discuss the present status of the celestial reference system and frame.

We discuss tools for implementing the recent IAU resolutions, notably the USNO Circular 179 and the NOVAS software package.

We discuss the issue of selecting highly-compact radio sources for the definition of the celestial reference frame.

We present a Véron & Véron based optical extragalactic reference frame progress report.

We discuss problems of the reference radio source selection.

We present a review of the Division I Working Group on Precession and the Ecliptic.

We discuss a long-term solution for the insolation quantities of the Earth.