A recent paper from the lab of Nobel Laureate Jack Szostak describes some of the best current solutions to some big problems.
Problem 1) Homochirality: Biology is universally homochiral.
Solution: Circular polarized light from interstellar molecular clouds can give amino acids an enantiomeric excess, irradiated iron ore can also tilt the balance of chirality, and grinding crystals can amplify chirality.
Problem 2) Nucleic acids don't spontaneously arise prebiotically.
Solution: Mix cyanamide and glycolaldehyde, let sit overnight, then add glyceraldehyde, incubate overnight, react with cyanoacetylene in a buffered aqueous solution of pH 6.5, then phosphorylate with urea and ammonium salts under heat, dehydrate and rearrange via intramolecular nucleophilic substitution, then cool, rehydrate and irradiate with ultraviolet light. Repeat.
There is no known way to spontaneously generate purines, but when one is found, we should be able to polymerize them on montmorillonite clay under strongly dehydrating conditions.
Problem 3) Concentration
Solution: Tide pools capture amino acids, dehydrate and condense. Freezing also condenses products between crystal grains as does adsorption on metal hydrides. Also the temperature gradients present around freshwater hydrothermal vents provide a concentration mechanism as well as a good place to make fatty acid vesicles. Which leads to the fourth problem:
Problem 4) Cellular replication
Solution: Montmorillonite clay. It catalyzes the formation of fatty acid vesicles. Using fatty acids from meteorites, the vesicles can capture self replicating RNA molecules and give them a safe place to grow. Then they can grow, capture amino acids and fatty acids from the environment, and if they grow in a solution of highly charged molecules the bubble will become a long skinny bubble, and if agitated it will break into two or more bubbles. Replication.
Problem 5) Genome replication
Solution: Fatty vesicle must be permeable, requiring the right mix of fatty acids, glycerol monoesters and
fatty alcohols, to allow raw materials to enter the protocell. Once replication is achieved, thermal cycling can seperate the newly replicated copy, perhaps in a cold pond with a local geothermal feature.
Problem 6) Emergence of complexity
Solution: Darwinian evolution and deep time.
We now have a picture of how life may have developed under prebiotic conditions. One can easily envision a scenario in which the earth was bombarded by meteorites containing amino acids, organic compounds and fatty acids which had passed through the circular polarized light of an interstellar molecular cloud, then cyanamide and glycolaldehyde were mixed in a freshwater tide pool and allowed to sit overnight, glyceraldehyde was then added and allowed to incubate overnight before reacting with cyanoacetylene in another tide pool containing a buffered aqueous solution of pH 6.5, then phosphorylated with urea and ammonium salts under heat, dehydrated and rearranged via intramolecular nucleophilic substitution before being allowed to cool and rehydrate and subsequently bathe in ultraviolet light. Once all the necessary nucleotides were present they were concentrated around freshwater thermal vents covered with montmorillonite clay and metal hydride which was occasionally exposed to the air for dehydration and concentration. Once in sufficient concentrations after a few freezing cycles and subsequent grinding, chunks of montmorillonite clay were scooped into fatty bubbles where they began to polymerize in the relative safety of their protective bubble of fat. Then when the molecules started replicating and the bubbles allowed more raw materials to permeate their fatty membranes, highly charged molecules caused the bubbles to become long and skinny which made them break and form tiny "baby" bubbles which continued to grow as long as they remained in a cold pond with a local geothermal feature nearby. Then Darwinian evolution took over and facilitated the complex machinery which we find in modern cells.
Of course, there are still a few unanswered questions.