In the beginning there was darkness and then BANG! giving birth to an endless expanding existence of time, space and matter. Now we can see further than we have ever imagined, beyond the limits of our existence in a place we call the Universe.Our universe is brimming with its strange violent and potentially life transporting phenomenon. Its like imagining cosmic puddles where objects could disappear being injected or escaped to some other place in space or time.These cosmic puddles are like tickets to oblivion for the most part. Because either you get shredded in a black hole or get torn apart in a gravastar. The first discussion about this cosmic puddle like phenomenon appeared in 1783, when former Cambridge don John Michel presented the following argument that if one fires a cannonball vertically upwards, its ascent will be solved by gravity and eventually the particle will stop moving upward and will fall back. But if we fire this cannonball with initial velocity greater than a critical value called escape velocity, the cannonball will get rid of the gravitational force applied and will get out of the area of its effect. The escape velocity for earth is about 12km\s and about 618km\s for the sun. Michel further argued that there could be stars that are much more massive than sun and have escape velocities greater than the speed of light. We would not be able to see these stars, because any light they sent would be dragged back by the gravity of these stars. Thus they would be what Michel called dark stars and we now call black holesThe idea of black hole dates back to the First World War, when German Astronomer Karl Schwarzschild solved equations of Einstein's newborn Theory of gravity while serving in Russian Front.From his achievements he showed that space-time around any massive star would be curved. It can be explained as if we squeeze a massive star like sun to have it concentrated into a one solar mass (MΘ) black hole with radius of only two miles. Like this the gravity of a star would be infinite and curvature of space time around it would spiral out of control. This implies that not only black hole is unique in being its mass concentrated into a tiny space but also unique in the way its gravity works, So as that not even photons can escape its grasp.The Black hole property of Schwarzschild's solution was recognized slowly as progress in understanding black holes was slow----people were unwilling to accept that physical objects would ever collapse to such an extreme state. Another stumbling block rested on a mathematical misunderstanding springing from the obvious fact that in usually adopted Schwarzschild Coordinate the metric becomes singular at the event horizon r = rs = 2GM/C2 (where M is the mass of black hole and 'rs' represents Schwarzschild's radius) Also a further cause for the delay in the understanding came from the fact that people did not seem to pay much attention to this discoveries reported by other people.One discovery which was found to be a rather incredulous was Chandreshakhar's alarming result of 1931, that because of relativistic degeneracy of electrons, a cold body could not prevent having mass more than 1.44~MΘ( Where MΘ denotes the mass of sun) from collapsing indefinitely. When later the alarm caused by the discovery subsided, Chandrasekhar was awarded a Noble Prize in 1983. It was at least in part for his early work on the limiting mass of cold stars.However, Chandrasekhar's work caused conspiracy among renowned scientists of that time like Sir Arthur Eddington and Einstein himself. They did not believe like most other scientists that laws of Physics would ever allow the singularity of condensed matter at such an extreme state.Despite these hindrances of getting science community to believe that black hole is not just a mathematical fantasy but is a real fact based on real laws of physics and nature. And for that observational research had to wait longer, untill the development of radio astronomy (from 1940's onwards) and X-ray astronomy (from 1960's onwards).One way of looking for a black hole was therefore to look for matter that was orbiting what seemed to be an unseen object . And taking this understanding into account the modern epoch of understanding black holes commenced in 1950's . Partly from the introduction of the idea idea that in coordinate systems metric is regular everywhere except at the origin (of which the Kruskal metric is best known) and partly from John Wheeler who coined the term black hole for the collapsed state of matter in 1969 and then conjectured that black holes have no hair; which meant that the collapsed state of any non-rotating massive star could in fact be described by Schwarschild's solution. Other highlights were Kerr's discovery of an exact solution for rotating black holes, and Israel's uniqueness theorem for non-rotating black holes soon to be extended by Carter and others to the rotating case. Another spectacular result was work that Roger Penrose did between 1965 and 1970, showing that according to general relativity there must be a singularity of infinite density within the black hole. It was rather like the big bang at the beginning of time only it would be end of time for collapsing body. At that singularity, our ability to predict the future breaks down. However any observer who remained, would not be affected by this failure of predictability because neither light nor any other signal can reach them from the singularity which can be concisely called the Penrose's singularity theorem. This result was soon extended by the Hawking and by Geroch.With hindsight, we can say that once it was understood what the appropriate level of mathematical sophistication is to adopt for great complex research on Black holes. As young physicists and mathematicians started to take interest in this field, taking the fact into account that work had to be done on had started to become prolific ------consequently great discoveries were made in 1950’s and 1960’s. Nevertheless there was still a chock to come, when Stephen Hawking presented his achievements named as Hawking radiation. This work explained that there are rays emitting out of black holes when quantum effects are taken into consideration and which permits a black hole thermodynamics to set up.So where do we stand on the question of whether black holes as described by the mathematical solutions discussed above actually exist in nature?What are the circumstances in which astrophysical black holes are thought likely to be formed? The mean density ‘ρ’ of black hole (its mass M divided by 4/3 πrs3) is proportional to 1/M2.For 1MΘ black hole, ρ ~ 1016 g/cm3, forty times nuclear matter density. Whereas for a black hole of 108 MΘ, ρ ~ 1g/cm3 the density of matter. Except this, it is crucial to note that conditions required for matter to form a small black hole are much more extreme than for a large one. There are three main regimes of black holes.(i) Stellar mass black holes formed after the death of some normal star.(ii) Supermassive black holes (~106-1016MΘ) formed in the centre of galaxies as a result of the processes of galactic dynamics.(iii) Black holes formed as a result of fluctuations or phase transitions in the early universe where conditions were so extreme that black holes of all masses would have been produced.However, scientists are concentrating more on stellar mass black holes based on their observational evidences found in the systems like Cygnus X-1, Scorpio X-1 and so many others.The discovery of the system Cygnus X-1 gave evidence of black hole emitting X-rays (By the end of 1960’s) . While the discovery of system Scorpio X-1 in 1966 gave proof of existence of an observed star and neutron star.Astronomers have also found convincing existence for a supermassive black hole in the centre of the giant elliptical galaxy M87, as well as in other galaxies. The discovery is based on velocity measurements of a whirlpool of hot gases orbiting the black hole. In 1994, Hubble Telescope data produced an unprecedented measurement of the mass of an unseen object at the centre of M87. Based on the kinetic energy of the material whirling about the centre, the object is about 3 billion times the mass of our sun and appears to be concentrated into a space smaller than our solar system.However, few scientists have questioned the existence of black holes and suggested in their place, the existence of an exotic bubble of superdense matter, an object they call a gravastar. Gravastars are cold, dense shells supported by a springy, weird space inside. These black holes critics suggest they are like black holes, lit only by the material raining down onto them from outside. In fact, they seem to fit all the observational evidence for the existence of Black holes.But the problem with idea of gravastar (appeared most recently in 2002) have some confused as well as mathematical problems under the carpet and needs much more explicit explanation. While black holes on the other hand not only have refuted the critics of Karl Schwarzschild and Chandreshaker but also have proved to be useful in predicting the future under the newly grasped idea of P-Branes and also for the establishment of theory of everything.