L. Testi (European Southern Observatory, Germany & INAF-Arcetri, Italy),
S. Andrews (Harvard-Smithsonian Center for Astrophysics, United States),
T. Birnstiel (Harvard-Smithsonian Center for Astrophysics, United States),
J. Blum (Institut für Geophysik und extraterrestrische Physik, TU Braunschweig, Germany),
J. Carpenter (California Institute of Technology, United States),
C. Dominik (University of Amsterdam, the Netherlands),
A. Isella (California Institute of Technology, United States),
A. Natta (Dublin Institute for Advanced Studies, Ireland & INAF–Arcetri, Italy),
L. Ricci (California Institute of Technology, United States),
J. Williams (University of Hawaii, United States),
D. Wilner (Harvard-Smithsonian Center for Astrophysics, United States)

In the core accretion scenario for the formation of planetary rocky cores, the first step toward planet formation is the growth of dust grains into larger and larger aggregates and eventually planetesimals. Although dust grains are thought to grow from the submicron sizes typical of interstellar dust to micron size particles in the dense regions of molecular clouds and cores, it is at the high densities reached on the protoplanetary disks midplane that the growth from micron size particles to pebbles and kilometre size bodies has to occur. This is a critical step for the formation of planetary systems and the last stage of solids evolution that can be observed directly in young extrasolar systems before the appearance of large planetary-size bodies. Tracing the properties of dust in the disk midplane, where the bulk of the material for planet formation resides, requires sensitive observations at long wavelengths (sub-mm through cm waves). At these wavelengths, the measured dust opacity can be related to the grain size distribution. In recent years the upgrade of the existing (sub-)mm arrays, the start of ALMA Early Science operations and the upgrade of the VLA have allowed a significant progress in our ability to provide observational constraints to the models of dust evolution in protoplanetary disks. Laboratory experiments and numerical simulations have allowed us to improve the understanding of the physical processes of grain-grain collisions, which are the foundation for the models of dust evolution in disks. In this chapter we cover the available constraints on the physics of grain-grain collisions as they emerge from laboratory experiments and numerical computations. We then review the status of our theoretical understanding of the global processes governing the evolution of solids in protoplanetary disks. We discuss the results of dust settling and growth and the radial transport of grains, as given by different dust evolution models, from fractal to compact growth, and outline the predicted observable signatures of these effects. We summarize how the dust opacity depends on the properties of the dust grains, as this is the property that links the theoretical evolution models with observational characteristics. We discuss the recent developments in the study of grain growth in molecular cloud cores and in collapsing envelopes of protostars as these likely provide the initial conditions for the dust in protoplanetary disks. We then discuss the current observational evidence for the growth of grains in young protoplanetary disks from millimeter surveys, as well as the very recent evidence of radial variations of the dust properties in disks. We also include a brief discussion of the constraints on the small end of the grain size distribution and on dust settling as derived from optical, near-, and mid-IR observations. The observations are discussed in the context of global dust evolution models, in particular we focus on the emerging evidence for a very efficient early growth of grains in disks and the radial distribution of maximum grain sizes as the result of growth barriers in disks. We will also highlight the limits of the current models of dust evolution in disks including the need to slow the radial drift of grains to overcome the migration/fragmentation barrier. Recent results from ALMA observations of grain growth in disks around brown dwars and transitional disks are also included.

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