Twenty years ago, it seemed reasonable that dark matter might consist of faint stars, substellar objects, or stellar remnants (white dwarfs or neutron stars), i.e., stars that simply were too faint to have yet been discovered. These fall into the category of massive compact halo objects, or MACHOs. Other MACHO candidates would include primordial black holes or mirror matter. 
A combination of theory and observation have ruled these out as solving the dark matter problem of the Milky Way. First, Refs. 19, 20 used HST data to show that low mass stars could be at most 3% of the Milky Way dark matter. Next, a combination of theory plus Hipparchos parallax data was used to rule out substellar objects, or brown dwarfs, as the primary constituent of the Galaxy's dark matter.  Stellar remnants were also potential DM candidates. Bounds on white dwarfs (WD) as dark matter came from many arguments (see Refs. 22, 23 for a review). Stellar precursors of white dwarfs would have produced too much IR radiation that would have swallowed TeV gamma-rays seen from objects like Markarian 451; a too large fraction of the Universe's baryonic mass budget would have been required to produce the progenitor stars of the white dwarfs; WD would have overproduced carbon and nitrogen. From these constraints we argued that at most 15% of the Milky Way Halo could be made of white dwarfs (Freese et al.,  Fields et al., , Graff et al. ); at that time we disagreed with claims made by the MACHO microlensing experimental that 100% of the dark matter could be in the form of MACHOs (the experiments originally overestimated the MACHO contribution).
Microlensing experiments (the MACHO (Alcock et al. ) and EROS experiments (Ansari et al. )) eventually showed that MACHOs less massive than 0.1 M⊙ make an insignificant contribution to the energy density of the Galaxy. However, there is a possible detection (Alcock et al. ) of a roughly 15% halo fraction made of ∼ 0.5 M⊙ objects which might be made of stellar remnants such as white dwarfs. These estimates agree with the numbers we found earlier from a combination of theory and other data sets. [22, 23] The white dwarf contribution to the dark matter halo could be significant, yet not enough to explain all of the dark matter of the Milky Way.
4.2. Nonbaryonic Dark Matter
From primordial nucleosynthesis and microwave background data, it has become clear that dark matter consists of nonbaryonic material. There is a plethora of dark matter candidates. Of the many candidates, the most popular are the weakly interacting massive particles (WIMPS) and the axions, as these particles have been proposed for other reasons in particle physics. These are discussed further below. Ordinary neutrinos are too light to be cosmologically significant, though sterile neutrinos remain a possibility. Other candidates include primordial black holes (for the latest bounds, see 29), self-interacting dark matter, light dark matter, asymmetric dark matter, nonthermal WIMPzillas, Q-balls, and many others.
The good news is that cosmologists don't need to “invent” new particles. Two candidates already exist in particle physics for other reasons: axions and WIMPs. Axions arise in the Peccei-Quinn solution to the strong-CP problem in the theory of strong interactions,  and are suitable dark matter candidates [31, 32] if the mass lies in the range ma ∼ 10−(3−6) eV. An upper bound on the axion mass ma < 15 meV can be derived from astrophysical considerations, [33, 34, 35, 36] while a lower bound comes from cosmology [37, 38, 39] and its value strongly depends on the thermal history of the universe and on the amount of topological defects.  An exclusion region 6 × 10−13 eV < ma < 2 × 10−11 eV that is independent of the cosmological history and comes from black hole super-radiance has been obtained  using aLIGO measurements. Microwave cavity searches  allow for a direct detection of axions. The Adark matterX cavity experiment (ADMX)  has already excluded a portion of the axion mass range and is currently searching for axions with a mass ∼ 10−5 eV. A different technique consisting of searching for keV photons from axion-photon conversion in the Sun (through the Primakoff effect) has also been used in the KEK, CAST, and IAXO observatories. Such “axion helioscopes” are sensitive to the heavier end of the axion mass window. In addition, new ideas for axion searches include the Cosmic Axion Spin Precession Experiment (CASPEr)  and broadband and resonant approaches.  Axion searches continue to reach into the theoretically best motivated regions of mass and coupling.
WIMPs are thought to be good dark matter candidates from particle physics for two reasons. They are defined to be particles that participate in weak interactions (but not strong or electromagnetic) and their masses are in the range GeV–10 TeV. These particles, if present in thermal abundance in the early universe, annihilate with one another so that a predictable number of them remain today. The relic density of these particles comes out to be the right value:
Here h is the Hubble constant in units of 100 km/s/Mpc, and the annihilation cross section ⟨σ v⟩ann of weak interaction strength automatically gives the correct abundance of these particles today. This coincidence is known as “the WIMP miracle” and is the first reason why WIMPs are taken so seriously as dark matter candidates.
Secondly, WIMP candidates automatically exist in models that have been proposed to resolve problems in theoretical particle physics. These models contain WIMPs as a byproduct of the theory. For example WIMP candidates exist in supersymmetric models (SUSY), including the lightest neutralino in the minimal supersymmetric standard model. Supersymmetry in particle theory is designed to keep particle masses at the right value. As a consequence, each particle we know has a partner: the photino is the partner of the photon, the squark is the quark's partner, and the selectron is the partner of the electron. The lightest superysmmetric partner is a good dark matter candidate. Another type of WIMP exists in models of universal extra dimensions. In these theories all standard model fields propagate in a higher dimensional bulk that is compactified on a space that is TeV−1 in extent. Higher dimensional momentum conservation in the bulk translates in four dimensions to Kaluza-Klein (KK) number (with boundary conditions to KK parity). The lightest KK particle, known as the LKP, does not decay and is a WIMP candidate.  WIMP candidates are well-motivated from the point of view of particle physics and relic density; the key issue now is whether or not nature agrees with our theoretical prejudice. The experimental hunt for WIMPs is ongoing.