PAH (polycyclic aromatic hydrocarbons) are known and probable human carcinogens, found in wood and cigarette smoke, and to a lesser extent the exhaust of vehicles without catalytic converters.  Woodsmoke has been called a "witch's brew of carcinogens" because of all the PAH and toxic chemicals it contains.

Benzo[a]pyrene (B[a]P) a known human carcinogen, featured in the "every cigarette is doing you damage" TV adverts, is the most well known PAH.  Burning 10 kg of wood in a correctly-operated Australian heater emits as much BaP as in the smoke from 270,000 cigarettes.

The danger of breathing air containing several PAH, is estimated by scoring the PAH in terms of the number of cancers they cause, compared to the the same amount of B[a]P - this is known as the B[a]P equivalent, or B[a]P-eq - see Appendix.
The most dangerous PAH in wood and cigarette smoke are B[a]P and dibenz[a,h]anthracene (considered 1.1 times more  dangerous than BaP). Burning 1 kg of wood in a correctly-operated Australian heater emits as much dibenz[a,h]anthracene as in the smoke from 225,000 cigarettes.

The Australian National Pollutant Inventory (NPI) reports PAH emissions, in terms of the total B[a]P equivalent. Domestic solid fuel heating is at the top of the list (see right hand column). Only 10.2% of Australian households used wood heating (878,400 housholds, ABS data, March 2011), but the the B[a]P equivalent of their toxic PAH emissions is nearly twice as high as all the 16.4 million registered motor vehicles in Australia, implying that the average Australian woodheater emits more than 31 times as many toxic B[a]P-equivalents as the average vehicle. 
  Wood heaters tend to be used in residential areas, leading to a build-up of pollution where people live and breathe. In contrast, a significant proportion of emissions from vehicles are on roads away from urban areas, so are less likely to be inhaled or damage people's health.

Mothers' PAH Exposure -> Genetic Damage in Babies, reduced IQ on starting school, behavioural Problems & reduced white matter in the brain of 8 year olds
In developing countries, children whose mothers cook with wood (as opposed to kerosene) stoves have reduced IQ, memory and poorer social skills in  Belize, Kenya, Nepal and American Samoa, and also in Guatemala  
In New York and other developed countries, similar studies link PAH exposure (the main toxins in woodsmoke), to genetic damage in babies, reduced IQ on starting school, and showing effects on behavioural problems (anxiety, depression and attention deficit) at age 6-7.
   The research from the New York study published in March 2012 is important because it measured genetic damage in terms of DNA adducts specific to benzo[a]pyrene in umbilical cord blood, and also measured the mothers' exposure to PAH during the 3rd term of pregnancy. The study provided clear evidence that B[a]P exposure is linked to behavioural problems. The 41% of children with detectable B[a]P adducts in umbilical cord blood had a 4-fold increase in attention problems, and 2.6-fold increases in attention/hyperactivity problems and anxiety problems
   Research published in 2015 reports the results of brain scans of a representative sample from the original New York study group consisting of 20 children whose own PAH readings were below the median and 20 whose PAH levels were above it. All the children were about 8 years old when they underwent magnetic resonance imagery scans. Those scans showed that white matter was significantly reduced from normal volumes throughout the left hemisphere, an area that controls language and cognition, among other higher functions.
   In fact, the higher their prenatal exposure to PAH was, the more white matter was reduced and the more acute the behavioral and developmental problems were, the study found.
   Scientists don't know why the left side seemed to be affected more, but they suspect the compounds interfere with an early biochemical process that helps the fetal brain divide into slightly asymmetrical hemispheres.
   The damage, however, is not isolated to prenatal stages, or to the left hemisphere. Postnatal PAH exposure, measured at age 5, correlated with diminished white matter in areas of the prefrontal cortex of both hemispheres, the study found.
    "It's a double hit," Peterson said. "They have the abnormality from prenatal life throughout the left hemisphere and then on top of that they have this bilateral frontal hit from exposures around age 5."
    The 40 children were from nonsmoking homes and had little or no exposure to lead or insecticides that likewise have been linked to developmental and behavioral problems, according to the study. All were right-handed.

   The results of the above studies suggest that pregnant women should avoid any sources of B[a]P, including woodsmoke Women in this study were exposed to average ambient B[a]P concentrations less than 0.5 n/gm3, much lower than average wintertime B[a]P measurements of 1.3 ng/m3 at the Armidale creeklands, (an area with no chimneys).  Armidale residents living close to wood heaters that emit visible smoke are likely to be exposed to even higher levels of B[a]P.  One possible way to minimize potential damage from woodsmoke is to use HEPA filters in the house.
    The study that linked behavioural problems to genetic damage from B[a]P and maternal exposure to PAH also showed that high PAH exposure of the mothers (anything above 2.26 ng/m3) was linked to a 5 point reduction in IQ on starting school.  With a second study in Poland also linking PAH exposure to reduced IQ of young children, measured wintertime PAH in Armidale (creeklands average 8.62 ng/m3, maximum 24.0) is of great concern, suggesting a significant risk that PAH exposure from the city's woodsmoke could lead to genetic damage, reduced IQ and bahavioural problems in some children.
Yet another study linking autism to PM2.5 pollution Prof Frank Kelly, the director of the environmental research group at King's College London, discussed the links between air pollution and autism: "I think if it was this study by itself I wouldn't take much notice, but it's now the fifth that has come to the same conclusion."

A study published in 2017 expressed concerns about excess lung cancer risk from air pollution at primary schools in Cassino, Italy, being one order of magnitude higher than the maximum tolerable value (10−5, according to the U.S. Environmental Protection Agency) due to the presence of biomass burning heating systems and winter thermal inversion that cause larger doses and great amount of toxic compounds on particles. The published paper reports average BaP concentrations in Cassino of 0.71 ng/m3 - suggesting similar concentrations to Armidale, NSW where BaP average 1.3 ng/m3 at the creeklands and most likely significantly higher concentrations in residential areas.
Appendix.  Estimates of the carcinogenic potential of various PAH, used in the Australian National Pollutant Inventory to calculate PAH emissions in terms of B[a]P-equivalents.  See Appendix E of the National Pollutant Inventory Guide to reporting.

Swedish Study showing a relationship between NO2 and PM10 pollution and mental health in children and adolescents (measured by whether or not the child had been given medication for a broad range of psychiatric disorders, e.g. sedatives, sleeping pills or anti-psychotic medications).   The authors conclude: "There may be a link between exposure to air pollution and dispensed medications for certain psychiatric disorders in children and adolescents even at the relatively low levels of air pollution in the study regions."

SF Bay Area Leaflet (click image to enlarge).  Air pollution causes water pollution.  Woodsmoke contributes 39% of dioxin air emissions; the EPA lists the SF Bay as an impaired waterway, in part due to dioxin.

Pollutant emitted by forest fire causes DNA damage and lung cell death

When exposed in a laboratory to pollution levels comparable to those found in the atmosphere of the Amazon region during the forest and crop burning season, human lung cells suffer severe DNA damage and stop dividing. After 72 hours of exposure, over 30% of the cultured cells are dead.
The main culprit appears to be retene, a chemical compound that belongs to the class of polycyclic aromatic hydrocarbons (PAHs).