Using pictures and diagrams
In the classroom or lecture slides: "illustration for instruction"
You can use any picture or diagram in teaching if it is vital to show the image in order to teach about it ; This is a "fair dealing" exception and does NOT apply to illustrations to make your presentation more appealing or engaging. Accordingly you are not supposed to use high resolution images.
Other fair dealing can include setting exams and coursework. Critiquing or reviewing a model or chart is also likely to benefit from the fair dealing exception - though if you are publishing your work or producing a critique or review for commercial purposes, you would be advised to seek the rightsholder's permission. See the guide on Fair Dealing.
In all other circumstances you will need to either
Just because an image is free-to-view on the internet does not mean it is free to use: please check the Guide to Getting the most from Free Resources
Brand and Company Logos
Companies and organisations tend to be particularly protective of copyright and trademark rights in their brand logo and insignia
Fair Dealing exceptions require that the use of an image is necessary. It is usually hard to argue that the inclusion of a company logo is necessary when the company name could have been used instead. There is also the risk of creating the impression that the use of the logo implies affiliation or endorsement.
If you cannot clearly demonstrate that use of the logo is necessary for a fair dealing exception, then permission must be sought before using a company logo or brand image or insignia.
Note that the incidental copying of a logo is allowed (if you are copying a journal or newspaper article which includes a picture of a logo for example).
Note also that the logos and insignia for public bodies are excluded from the Open Government Licence and the Open Parliament LIcence.