Sen. David Brinkley (R-Frederick) wears a necktie emblazoned with the Maryland state flag on the opening day of the 2014 legislative session. (AP Photo/Patrick Semansky)

Many of the bills that Maryland lawmakers consider each year in Annapolis look familiar — and with good reason. It can take several sessions for some bills to pass, and some never will, despite the perennial efforts of their sponsors.

This week features an unusual number of committee hearings on bills that are back for another round of consideration.

And, of course, there will continue to be questions this week about the status of Maryland’s ailing online health insurance exchange.

Here’s a look at some of the things to watch:

Will legislation increasing penalties for smuggling cellphones into correctional institutions be viewed differently after the Baltimore jail scandal?

Maryland lawmakers have repeatedly killed legislation sought by corrections officials to crack down on the smuggling of cellphones into prisons, a key element of the gang culture that thrived in the Baltimore jail at the center of two rounds of federal indictments last year.

More than two dozen guards were alleged to have conspired with members of the Black Guerilla Family gang in drug and money-laundering schemes at the state-run Baltimore City Detention Center and an adjacent facility.

The legislature will start hearing a handful of bills this week intended to reduce the likelihood of similar activity in the future. Among those: a bill backed by the administration of Gov. Martin O’Malley (D) that would make it a felony rather than a misdemeanor to smuggle in a cellphone.

Opponents of similar legislation have argued in past years that branding cellphone violators as felons would have serious consequences for them, including a loss of voting rights and difficulty finding employment upon their release. And with the advent of cellphone-jamming technology, they question whether the legislation is necessary.

But O’Malley officials are pushing for the legislation again, arguing that cellphones continue to be used by inmates to plot criminal activity inside and outside the institutions where they are confined.

The bill is scheduled to be heard Tuesday by the House Judiciary Committee, along with other legislation targeting cellphones that was drafted by a special committee formed in the wake of the Baltimore scandal and by Del. John W.E. Cluster Jr. (R-Baltimore County), a retired police officer.

Will the General Assembly find a way forward on dog bites?

Dogfights are coming to Annapolis again, as lawmakers continue a nearly two-year search for a way to deal with questions of liability in dog-bite cases.

Until a 2012 ruling by the state’s highest court, Maryland operated on the “one bite” principle: The owner of a dog that bit someone could not be held liable so long as the dog had never shown a history of violence. In April 2012, however, the Maryland Court of Appeals singled out pit bulls as an inherently risky breed, making their owners and landlords almost automatically responsible when a dog bites someone.

Since then, the legislature has been struggling to find a balance that would satisfy dog lovers who think their pets are under fire as well as people who have been harmed by dogs.

This year, lawmakers have filed several bills, including a measure sponsored by Del. Luiz R.S. Simmons (D-Montgomery) that would create the presumption that the owner knew or should have known the dog was vicious. But the bill would also give the owner an opportunity to undercut that presumption by presenting evidence that the dog had no history of violence.

On Thursday, the Senate Judicial Proceedings Committee will hear testimony on bills submitted by Sens. Brian E. Frosh (D-Montgomery) and Robert A. Zirkin (D-Baltimore County).

Frosh’s bill is the Senate version of Simmons’s legislation. Zirkin’s bill would put the onus on the dog owner regardless of the animal’s breed, unless there was evidence that the victim provoked the attack. His bill would also prohibit insurers from refusing to pay a claim based on the breed of the dog.

Though the bills differ in their aims, they all share the intent of undoing the Court of Appeals ruling.

“The court decision, in my opinion, is bad. Whether you get attacked by a pit bull or a Chihuahua should be the same exact standard,” Zirkin said. “If you are blameless, then the owner should be responsible for the damage done — not the blameless victim.”

Will a hearing on legislation offering protections for transgender people be a preview of a key Montgomery County Senate race?

A bill that would give greater protection to transgender people will set up a public encounter between the openly gay senator who is sponsoring the bill and the transgender candidate who announced her candidacy against him last week.

The bill, sponsored by Sen. Richard S. Madaleno Jr. (D-Montgomery), would prohibit discrimination based on “gender identity” in the workplace, housing and public accommodations. The bill defines “gender identity” as the gender-related identity, appearance, expression or behavior of an individual regardless of the individual’s biological sex at birth.

Dana Beyer, a former Montgomery County Council aide, said that as executive director of Gender Rights Maryland, she plans to testify at the hearing before the Senate’s Judicial Proceedings Committee on Tuesday.

Will a debate over smoking in cars with young children end any differently this year?

Del. Benjamin S. Barnes (D-Prince George’s) is scheduled to make his pitch Wednesday to the House Economic Matters Committee for legislation that would prohibit drivers from smoking in their cars if they have a passenger under age 8.

Similar bills have been introduced since 2007 but have never made it to the governor. For the past two years, the Senate passed its version of the legislation but the House didn’t budge.

Proponents say the measure is necessary to protect defenseless children from the dangers of secondhand smoke. But opponents have cast the issue in terms of parental rights and argue that it would be difficult to enforce.

Violators would be subject to a $50 fine.

Will the health insurance exchange enrollment numbers pick back up?

Each Friday, Maryland health officials release the latest number of residents who have enrolled in a qualified health insurance plan through the state’s new exchange. O’Malley originally aimed to get at least 150,000 Marylanders signed up during the first open-enrollment period, which started Oct. 1 and will end March 31.

That goal has been slowed by a malfunctioning online marketplace that crashed on its first day and has been plagued with problems ever since, making it difficult for residents to enroll.

The first enrollment report in mid-October stated that just more than 1,000 people had enrolled. For weeks the number slowly grew, but not by much. As the end of 2013 approached — following a slew of site improvements — there was a rush of sign-ups. One week there were 4,280 more enrollees. The next, more than 6,500.

But for the past month, the number of new weekly enrollees has been in the 2,000 range. The latest enrollment report, released Friday, showed a bump of just 1,655. The total number of residents enrolled now sits at 26,832. Two months remain before enrollment will close, and it remains to be seen if the numbers will start to pick up momentum.