Fresh wood products like sawdust or pine needles or bark are great organic mulches. They keep down most weeds, regulate soil temperatures, attract many benneficial soil organisms, and are usually free or very cheap to get.
However, there is some concern about the high acidity of products like pine needles and sawdust. Also some wood products made from black walnut trees can be allelopathic, due to the release of toxin products like juglone in the soil. There is also the concern of temporary nitrogen deficiencies in the soil near growing plant roots, because wood products are usually high carbon materials.
If your wood products are well aged, over 6-12 months old, in most cases, any of the above issues are meaningless. Of course there are a few exceptions with some controversial wood products like black walnut tree products.
The same is true if your compost any wood products with other "browns" and "greens", through a hot process, where internal temperatures exceed 140 degrees F, for several days, with constant aeration and moisturizing through the composting process. The resulting mature compost will have a near neutral pH, with all the mild toxins neutralized and balanced with other available soluble nutrients, so that your plants can grow safely and healthy in the soil. Good, active, highly aerobic, hot composting usually heals and breaks downs all issues that most gardeners have with controversal organic materials.
If you keep enough mature compost or high nitrogen organic matter mixed in your soil underneath, even with using fresh acidic woody mulches, there will be no visible signs of nitrogen deficiencies, or soil pH issues, to your growing plants using these types of mulches. Nitrogen deficiencies are caused by high carbon materials in the soil, reacting with soil microbes, fighting to maintain the near 30:1 carbon-nitrogen ratio that they need to survive and grow as they benefit our soils, and for organic matter decomposition.
All organic matter made from trees is rich in total calcium and potassium. Even wood ashes, can contain up to 70% calcium carbonate or calcium oxide (liming agents), and is rich in available potassium.
NOTE: Never use wood ashes directly in your soil, if you haven't recently checked your native soil pH! Don't use wood ashes in your compost pile too much (Only use it if you have an abundance of ashes that you need to get rid of, or use in your gardening schemes). Wood ashes will chemically react with high nitrogen materials like fresh animal manures, and waste off a lot of your valuable nitrogen in the pile off as ammonia gas. Also any liming agent is not necessary in an active compost pile anyway. Compost will naturally go up and down in pH from very acidic, to very alkaline, to a resulting near neutral pH, as aerobic microbes break down and digest organic matter in the pile over time.
Composted or well aged sawdust is also a powerful soil conditioner. It is better and cheaper than gypsum for aerating and loosening up native heavy clay soils. The extra calcium and potassium benefits are great assets also. Earthworms and soil microbes love it!
In conclusion, using wood products as mulches or composting ingredients, is some of the best stuff in the world to use for soil building. Like everything else, use them wisely.
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