Electromagnetic channel – From the observational point of view, the electromagnetic channel is essentially the only one efficiently used for the moment. Indeed, X-ray spectroscopy and continuum fitting methods have given some insight on the spin of massive BHs. The spin distribution of BH contains important information about how they accrete matter. Supermassive BH’s spin seems to range from Kerr parameter ~.2 -.998. In fact, these measures are still under controversy, and eLISA (see below) will be more than helpful to settle the issue. Remarkably, pulsar timing arrays may have the potential to detect GW. This technique has been originally introduced to study diffuse stochastic backgrounds but it has been recently applied to detect the early inspiral of massive BH binaries . Such method allows to measure the mass and distance of binary BH and GW signal might even already be present in currently available pulsar timing array data . NS are already observed with space-based telescopes such as Chandra in the X-ray regime and estimations for the radius are derived, though still not reaching consensus. On another hand, over the next decade, upcoming experiments such as the Neutron-Star Interior Composition Explorer (NICER), the Large Observatory For X-ray Timing (LOFT)  and the Horizon Telescope will uncover regimes never accessed before and likely lead to invaluable insights in compact object physics. Let us stress the European project ATHENA-X, which has been selected as second Large project (L2) by the Cosmic vision program of the ESA. ATHENA-X, for Advanced Telescope for High ENergy Astrophysics, will explore the X-ray universe with an angular resolution of 5 arcsec and will probe the universe out to a redshift z=10. See  for some project web pages.
Gravitational Channel – In parallel, the gravitational wave channel will likely be explored during this century. Gravitational waves allow to probe the most extreme regime of gravity, without requiring luminous electromagnetic sources. The most promising sources for gravitational waves are binary systems. The signal is essentially unperturbed from ambient matter and the signal reaching the earth is clean, contrary to electromagnetic signals which are distorted by their environment. The first generation of ground-based gravitational wave interferometers have reached their design sensibility some years ago (see LIGO, VIRGO). For instance, the European ground based detector VIRGO is composed of two 3 km long arms and is based on the same principle as the Michelson interferometer. The experiment had its first science run in 2007. Improved detectors such as aLIGO, aVIRGO will start operating in the next few years. Third-generation detectors like the Einstein Telescope or KAGRA are currently under study. Additionally, space-based observatories are planned, such as the eLISA mission  which is the best candidate for the L3 mission of the Cosmic Vision program. It will be sensitive to low frequency GW and is expected to start operations in the next few decades. While the earth based detectors will be sensitive to the frequency region from few Hz to 10 kHz, the space based antenna will cover the low frequency regime. “Astrophysical” sources emit mainly in higher frequencies while super-massive black holes will be potentially seen by space-based observatories. The present, planed upgrades and upcoming GW observatories will cover almost all the frequency regimes relevant for CO physics. See  for some GW detector project web pages.
 Gillessen, S., Eisenhauer, F., Trippe, S., Alexander, T., Genzel, R., Martins, F., and Ott, T. (2009). Monitoring Stellar Orbits Around the Massive Black Hole in the Galactic Center. apj 692, 1075-1109.
 Brenneman, L.W., and Reynolds, C.S. (2006). Constraining Black Hole Spin Via X-ray Spectroscopy. Astrophys.J. 652, 1028-1043.
 Stergioulas, N., and Morsink, S. (). RNS code, http://www.gravity.phys.uwm.edu/rns/. .
 Hartle, J.B. (1967). Slowly rotating relativistic stars. 1. Equations of structure. Astrophys.J. 150, 1005-1029.
 Regge, T., and Wheeler, J.A. (1957). Stability of a Schwarzschild singularity. Phys. Rev. 108, 1063-1069.
 Mano, S., and Takasugi, E. (1997). Analytic solutions of the Teukolsky equation and their properties. Prog. Theor. Phys. 97, 213-232.
 Leaver, E.W. (1986). Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two‐center problem in molecular quantum mechanics. J. Math. Phys. 27, 1238-1265.
 Berti, E., Cardoso, V., and Starinets, A.O. (2009). Quasinormal modes of black holes and black branes. Class. Quant. Grav. 26, 163001.
 Kokkotas, K.D., and Schmidt, B.G. (1999). Quasi-normal modes of stars and black holes. Living Rev. Relativity 2, 2.
 Lau, H., Leung, P., and Lin, L. (2010). Inferring physical parameters of compact stars from their f-mode gravitational wave signals. Astrophys.J. 714, 1234-1238.
 Tsui, L., and Leung, P. (2005). Universality in quasi-normal modes of neutron stars. Mon. Not. R. Astron. Soc. 357, 1029-1037.
 Yagi, K., and Yunes, N. (2013). I-Love-Q: Unexpected Universal Relations for Neutron Stars and Quark Stars. Science 341, 365-368.
 Maselli, A., Cardoso, V., Ferrari, V., Gualtieri, L., and Pani, P. (2013). Equation-of-state-independent relations in neutron stars. Phys. Rev. D 88, 023007.
 Pappas, G., and Apostolatos, T.A. (2013). Universal behavior of rotating neutron stars in GR: Even simpler than their Newtonian counterparts. .
 Doneva, D.D., Yazadjiev, S.S., Stergioulas, N., and Kokkotas, K.D. (2014). Breakdown of I-Love-Q universality in rapidly rotating relativistic stars. Astrophys. J. Lett. 781, L6.
 Chakrabarti, S., Delsate, T., Gürlebeck, N., and Steinhoff, J. (2014). The I-Q relation for rapidly rotating neutron stars. Phys.Rev.Lett. 112, 201102.
 Banados, M., and Ferreira, P. (2010). Eddington’s theory of gravity and its progeny. Phys. Rev. Lett 105, 011101.
 Sham, Y.H., Lin, L.M., and Leung, P. (2014). Testing universal relations of neutron stars with a nonlinear matter-gravity coupling theory. Astrophys. J. 781, 66.
 Collins, H., Holman, R., and Ross, A. (2012). Effective field theory in time-dependent settings.
 Goldberger, W.D., and Rothstein, I.Z. (2006). An effective field theory of gravity for extended objects. Phys. Rev. D 73, 104029.
 Goldberger, W.D., and Ross, A. (2010). Gravitational radiative corrections from effective field theory. Phys. Rev. D 81, 124015.
 Goldberger, W.D., and Rothstein, I.Z. (2006). Dissipative effects in the worldline approach to black hole dynamics. Phys. Rev. D 73, 104030.
 Blanchet, L. (2011). Post-Newtonian theory and the two-body problem. Fundam. Theor. Phys. 162, 125-166.
 Poisson, E., Pound, A., and Vega, I. (2011). The Motion of point particles in curved spacetime. Living Rev.Rel. 14, 7.
 Bel, L., Damour, T., Deruelle, N., Ibanez, J., and Martin, J. (1981). POINCARE INVARIANT GRAVITATIONAL FIELD AND EQUATIONS OF MOTION OF TWO POINT – LIKE OBJECTS: THE POSTLINEAR APPROXIMATION OF GENERAL RELATIVITY. .
 Blanchet, L. (2006). Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries. Living Rev. Relativity 9, 4.
 Love, A.E.H. (1911). Some Problems of Geodynamics. Cambridge University Press, Cambridge, England.
 Damour, T., and Nagar, A. (2009). Relativistic tidal properties of neutron stars. Phys. Rev. D 80, 084035.
 Binnington, T., and Poisson, E. (2009). Relativistic theory of tidal Love numbers. Phys. Rev. D 80, 084018.
 Kol, B., and Smolkin, M. (2012). Black hole stereotyping: Induced gravito-static polarization. JHEP 1202, 010.
 Sesana, A. (2013). Gravitational wave science with laser interferometers and pulsar timing. Braz.J.Phys. 43, 314-319.
 McWilliams, S.T., Ostriker, J.P., and Pretorius, F. (2012). The imminent detection of gravitational waves from massive black-hole binaries with pulsar timing arrays. .
 Feroci, M., den Herder, J.W., Bozzo, E., Barret, D., Brandt, S., Hernanz, M., van der Klis, M., Pohl, M., Santangelo, A., Stella, L., and et al. (2012). LOFT: the Large Observatory For X-ray Timing. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 8443.
 Amaro-Seoane, P., Gair, J., Freitag, M., Miller, M.C., Mandel, I., Cutler, C., and Babak, S. (2007). Astrophysics, detection and science applications of intermediate- and extreme mass-ratio inspirals. Class. Quant. Grav. 24, R113.