In the 1890s, electric bicycles were documented within various U.S. patents. For example, on 31 December 1895, Ogden Bolton Jr. was granted U.S. Patent 552,271 for a battery-powered bicycle with "6-pole brush-and-commutator direct current (DC) hub motor mounted in the rear wheel". There were no gears and the motor could draw up to 100 amperes (A) from a 10-volt battery.[5]
If you are a person who enjoys riding a bike casually at a typical bike path speed (10-15mph), and you like the idea of an ebike push up a hill, against the wind or to relieving a sore knee, then your market for a fully legally defined ebike is very broad and your practical use only has a few limitations. Most ebikes will meet your needs and expectation. I would estimate that 85% of the electric bikes on the market are 100% compliant meeting the federal definition. I encourage you to take the plunge and get a good quality ebike and ride more with assist. Do so with the confidence that electric bikes are here to stay. Coexisting with pedestrians and other cyclist will become a normal part of cycling life.
Your local state may have very definite rules as to what is an e-bike, what is a moped, and what is a motorcycle. While ebikes enthusiast don’t want the motor vehicle label, it is certain that each state will define some power level and speed where that classification will apply. Your best source of information is to go directly to your state motor vehicle department website, and get a copy of the your local state vehicle codes, with NO EDITING. Only recently updated official state vehicle codes will contain all the latest changes to the laws.1 For a link to your state MVA, look here:2

Class 1 makes great inroads to establish set boundaries for off road/natural surface trail access for eMountain bikes. There is fierce resistance from some mountain biking purists to allow ebikes on trails. BPSA and IMBA have done good work to justify the impact of class 1 ebikes on natural surface trails, and eliminate the wear-n-tear argument, though IMBA members are not 100% on board.

However, laws and terminology are diverse. Some countries have national regulations but leave the legality of road use for states and provinces to decide. Municipal laws and restrictions add further complications. Systems of classification and nomenclature also vary. Jurisdictions may address "power-assisted bicycle" (Canada) or "power-assisted cycle" (United Kingdom) or "electric pedal-assisted cycles" (European Union) or simply "electric bicycles". Some classify pedelecs as distinct from other bikes using electric power. Thus, the same hardware may be subject to many different classifications and regulations.
There are two basic categories of electric bike, and their uses don't offer equal crossover value. The first category is essentially a normal bicycle that has been outfitted with an electric motor. These bikes are the same size as a standard bicycle, and handle almost identically, save for the obvious benefit of added motive power thanks to a motor and battery.
^ Consumer Product Safety Act, Pub. L. 107–319, December 4, 2002; codified at 15 U.S.C. 2085(b): The CPSC regulations do not differentiate between commercially manufactured low speed electric bicycles and those converted from ordinary bicycles by their owners using an aftermarket electric motor and battery kit, nor do they regulate the construction of electric-power bicycles using owner-built or sourced components.
Historically, women's bicycle frames had a top tube that connected in the middle of the seat tube instead of the top, resulting in a lower standover height at the expense of compromised structural integrity, since this places a strong bending load in the seat tube, and bicycle frame members are typically weak in bending. This design, referred to as a step-through frame or as an open frame, allows the rider to mount and dismount in a dignified way while wearing a skirt or dress. While some women's bicycles continue to use this frame style, there is also a variation, the mixte, which splits the top tube laterally into two thinner top tubes that bypass the seat tube on each side and connect to the rear fork ends. The ease of stepping through is also appreciated by those with limited flexibility or other joint problems. Because of its persistent image as a "women's" bicycle, step-through frames are not common for larger frames.

Pedelec is a European term that generally referred to an electric bicycle that incorporated a torque and/or a speed sensor and/or a power controller that delivered a proportionate level of assist and only ran when the rider pedaled. On the opposite side, a Noped is a term used by the Ministry of Transportation of Ontario for similar type vehicles which do not have pedals or in which the pedals have been removed from their motorized bicycle. Finally, Assist Bicycle is the technical term used to describe such a vehicle and Power-Assisted Bicycle is used in the Canadian Federal Legislation, but is carefully defined to only apply to electric motor assist, and specifically excludes internal combustion engines (though this is not the case in the United States).
Controllers for brushed motors: Brushed motors are also used in e-bikes but are becoming less common due to their intrinsic lower efficiency. Controllers for brushed motors however are much simpler and cheaper due to the fact they don't require hall sensor feedback and are typically designed to be open-loop controllers. Some controllers can handle multiple voltages.
Bicycles are popular targets for theft, due to their value and ease of resale.[113] The number of bicycles stolen annually is difficult to quantify as a large number of crimes are not reported.[114] Around 50% of the participants in the Montreal International Journal of Sustainable Transportation survey were subjected to a bicycle theft in their lifetime as active cyclists.[115] Most bicycles have serial numbers that can be recorded to verify identity in case of theft.[116]
An itinerant wordsmith with a broad constellation of interests, Lydia Chipman has turned iconoclasm into a livelihood of sorts. Bearing the scars and stripes of an uncommon diversity of experience -- with the notable exceptions of joining a religious order or becoming an artist -- she still can’t resist the temptation to learn something new. Lydia holds a master of arts in English from Georgia Southern University, and a bachelor of arts cum laude in integrative studies from Clayton College. Her expertise is in the areas of robotics, electronics, toys, and outdoors and computer equipment.
Can I legally buy/build and ride an ebike that’s faster than 20 mph? Yes you can, but you need to know that the ebike is no longer considered equivalent to a bicycle and is subject to other state vehicular classifications. The definitions for electric bikes spanning 20-30mph, and 1-2 horsepower ranges, will vary from state to state, resulting in a no-man’s-land consensus about limits for motor vehicle definition. The common label for a 20-30mph, 2-wheeled vehicle with active pedals is a Moped. Other MVA labels include motor scooter, motorbike and dirt bike which may have equivalent power and speed performance, but do not have pedals to assist and move the vehicle.
Parliament has decided to approve the speed pedelec – a type of super electric bike that can reach speeds of up to 45 km/hour – for riding on cycle paths. Danish Parliament has decided that as of July 1 2018 those operating the super bikes only need to have turned 15 and wear a helmet, while the licence and number-plate demands will no longer be in play. [38]